Afrikaans/Print version


Afrikaans

Main Contents


Introduction

The youngest Germanic language

The name "Afrikaans" means literally "African". Afrikaans has its roots in 17th-century Dutch, but has since developed its own distinctive character and flavour in the three centuries that it developed mostly in South Africa and in parts of Namibia. Being a Germanic language, it is closely related to Dutch, English and to a lesser extent German. Compare the following:

  • English: I eat an apple.
  • Afrikaans: Ek eet 'n appel.
  • Dutch: Ik eet een appel.
  • German: Ich esse einen Apfel.

English has many more words of a Latin or French origin than Afrikaans, but a more archaic word can often show the similarities between the two languages.

  • English: hound, fowl, house, milk
  • Afrikaans: hond, voël, huis, melk
 
Provinces of South Africa where Afrikaans is in the majority. Note that Afrikaans is spoken all over the country and also in Namibia.

Most interestingly, consider these two sentences:

  • My hand is in warm water.
  • My pen is in my hand.

These two sentences can be either English or Afrikaans, and both have exactly the same meaning in both languages. But despite this, Afrikaans has significant differences from English. It might not be as easy to learn for an English speaker as, say, Esperanto, but it is still considered a relatively easy language to learn, and is advocated by some as a good introduction to learning Dutch and other Germanic languages in general.

Can Afrikaans people and Dutch people understand each other?

Afrikaans and Dutch are very closely related and are more or less mutually understandable. More about that here. Dutch's grammar is a bit more complex than Afrikaans', but they share a lot of the same vocabulary, albeit with slightly different spellings and pronunciations. Comparing Afrikaans and Dutch is somewhat like comparing Norwegian Bokmål and Danish.

It is a commonly held belief that Afrikaans people tend to understand Dutch quite well, and Dutch people generally need more time to understand Afrikaans. The truth of this claim may vary from individual to individual. Some Afrikaans people claim to understand written Dutch better than spoken Dutch.

Language of the oppressor?

Afrikaans is seen by some in a negative light because it was the language promoted by the apartheid regime. Some even claim that it should be forgotten. We acknowledge the terrible atrocities of that regime but still regard Afrikaans language and culture as beautiful and worthy of preservation. However, with regard to the sentiment of preservation of the language and culture, there remains an underlying tone of segregation as illustrated by the special interest groups: Afriforum; Solidariteit and the AfrikanerBond amongst others. The underlying segregationist sentiments of Afrikaner language and cultural proponents are along the lines of Hendrik Verwoerd's assertion of Apartheid as: 'Good Neighbourliness', which can be seen in the fact of the majority of Afrikaans Speakers being what, in South Africa, are called 'Coloured' people who are then represented as a minority in Afrikaans institutions and media such as the television channel KYKNET, radio RSG and newspapers like BEELD, Volksblad and magazines HUISGENOOT and ROOIROSE. What one sees then is that there is a concerted, if not wholly deliberate effort to present Afrikaans as the language of the majority of White South Africans in the same way that it had been prioritised in the 20th Century to aid the White Afrikaner Nationalism of the National Party; in its infancy in the 1910s to its introduction and preservation of Apartheid from 1948 until the introduction of the 1996 South African Constitution with its ideal of the equality of all languages.

Besides, more than half of the speakers of the language are not white and were victims of the regime's many manipulations, including ripping apart families and forcefully moving whole communities. As has been stated in the preceding paragraph, the complexity of understanding Afrikaans social presence in South Africa is dependent upon understanding what the language has been and what the attempts at it's rehabilitation are; while there remains an element of Afrikaner society that looks upon the history of Afrikaner people and the attending atrocities as something to look back upon, fondly, it is this aspect of the culture and the people that undercuts whatever is being done to disillusion afrikaans-speakers of claims of its superiority and importance over other South African languages if not English itself.

Additonally, some of the first literary works in Afrikaans were translations of holy Islamic texts by Abu Bakr Effendi that were used by the Muslim Cape slave population. Hence, the language can be equally be described as the language of the oppressed. Indeed, while there may be those who delude themselves in thinking that Afrikaans is the 'language of the oppressed', one cannot simply ignore the social environment in which 'the oppressed' came to speak Afrikaans in the first place as slaves who tried to manoeuvre their way across the Dutch language of their Slave masters. Afrikaans, then comes to be used as a way to distinguish those who created an identity out of propagating slavery and anti-equality in the Cape and further oppression down the centuries. How Afrikaans comes to be a Language in 21st Century South Africa is a fraught 200+ years history

Trivia

 
The Afrikaans monument.

<<Back to the main page

On to Pronunciation!>>


Pronunciation

Afrikaans uses the same alphabet as English. Notable differences include diacritics on the letters (like ê), while certain letters, such as c, exist but are infrequently used.

You'll soon find Afrikaans has a very phonetic (phonemic) spelling; that is, unlike in English, French or even its parent language Dutch, Afrikaans words are almost always spelled the way they sound.

This chart uses IPA - the international phonetic alphabet to show the exact Afrikaans pronunciation. You can read more about it here. The English words are only an approximate guide. Afrikaans pronunciation can be a bit tricky for English speakers because the language has quite a few sounds that don't exist in English. The best way to learn is to listen to native Afrikaans speakers. You can listen to streaming Afrikaans radio here and hear Afrikaans sound recordings at this site.

Letter IPA English Approximation Example Word
a ʌ, a, ɑː plus, jump, awesome kap
aa ɑː awesome daad
aai aːɪ why laai
ai thai baie
au ou goat auditorium
b b, p (final position) bat, mapp bevat
ch x loch chemie
c s (before e, i, and y), k sun, kick Celsius
d d, t (final position) dark, hat daar
dj c no English approximation djihad
e ɛ, iˑǝ, ə, æ bed, erie, about, cat bed
ê ɛː (final position), æ hair, cat
ee iˑe eerie een
eeu iːu east + took leeu
ei əi play seil
ey əi play ceylon
eu øː few euforie
f f fox familie
g x, g, ç loch, golf, hue geld
gh g, k (final position) golf, kick gholf
h h high hoe
i i, ə see, about idee
ie i see dankie
j j yes ja
k k kick kat
l l let lughawe
m m mall maak
n n, ŋ (before c, k, q, and x) nice, sing van
ng ŋ sing vang
ns the n is silent, and the previous vowel is nasalized no English approximation Afrikaans
o ɔ, oˑǝ bog, wisdom obligasie
ô ɔ cause môre
oe u loot voet
oei uiː phooey koei
oi oj row + yes boikot
oo uˑo loot soom
ooi ɔiː oil strooi
ou ɔʊ tow mou
p p map paar
r ɾ rolled r rooi
s s sun sein
sj ʃ shin sjoe
t t top taal
tj tʃ (initial position), kj top + shin, kick + yes tjek
u ɵ urn uit
uu y breed duur
û œː no English approximation brûe
ui œy play lui
uy œy urn + east ly
v f fox voël
w v, w (after consonant) visit, winter water
y əi play ys
z z zulu zirkonium

<<Back to Introduction

On to Lesson One!>>


Lesson One

Lesson One: The Basics #1 — Les Een: Die Grondbeginsels #1

Welcome to Afrikaans Lesson One. This course will focus heavily on translation and reading in order to further your knowledge in a shorter span of time. In far later lessons, we will start the lesson with the dialogues, but for now, we shall start with the grammar of the language. If you still need to practice basic Afrikaans pronunciation, we recommend using the Pronunciation page. This lesson will cover similarities between English and Afrikaans, the use of articles, subject and object pronouns, and infinitive and present tense verbs.

I. Similarities Between English and Afrikaans

As both Afrikaans and English stem from the West Germanic family, obvious similarities exist in syntax, vocabulary and word formation. This fortune allows for Afrikaans to be a simple language for English speakers to grasp.

Spelling Comparison

Apart from direct cognates, spelling patterns can be ascertained too. Though none of these rules are etched in stone and each word should be studied carefully, these commonalities definitely make acquiring certain Afrikaans words much easier.

  • The English suffix, -tion, often translates to the Afrikaans suffix, -sie.
    • Examples: posisie (position), aksie (action), kondisie (condition)
  • Some monosyllabic Afrikaans words containing the letter, g often correspond to an English, y. This trend continues with the particularly noticeable Afrikaans adjectival suffix, -ig.
    • 'G' Examples: geel (Yellow), dag (day), weg (way), vlieg (to fly), oog (eye)
    • '-ig' Examples: heilig (holy), sonnig (sunny), ysig (icy), besig (busy)
  • Some Afrikaans words beginning with sk-, are akin to English, sh-.
    • Examples: skip (ship), skaduwee (shadow), skoen (shoe)
  • If there are words that are the same in both languages, an English hard c is usually equivalent to an Afrikaans k with few exceptions:
    • Examples: kamoeflage (camouflage), kalamari (calamari)

II. Articles

The definite article in English is the, which in Afrikaans, is die.

  • Examples: "Die man" ('The man'); "Die kind" ('The child'); "Die rivier in die woud." ('The river in the forest.')

English's indefinite article, a/an both become ʼn (pronounced as [ə]) in Afrikaans. Whenever a sentence begins with the indefinite article, the spelling rule associated declares that the noun, proper noun or adjective that directly follows must be capitalized.

  • Examples: "ʼn Vrou" ('A woman'); "ʼn Tafel" ('A table'); "ʼn Seun en ʼn meisie." ('A boy and a girl.')

III. Pronouns: Subject and Object

A. Subject Pronouns (Nominative Case)

Person English Afrikaans English Afrikaans English Afrikaans
Singular Plural Formal
1st Pers.
I
ek
we
ons
2nd Pers.
you
jy
you
julle
you
u
3rd Pers.
he
she
it
hy
sy
dit
they
hulle

Afrikaans, like English, follows a simplistic SVO (Subject - Verb - Object) word order. The subject of a sentence refers to who/what is doing an action.

  • I know him.' → "Ek ken hom."

Though the subject rules are essentially the same as in English, there are two things to note on formality of conversation:

  1. When in an informal context, julle and hulle can be shortened to jul and hul.
    • 'They talk to him.' → "Hulle praat met hom." is the same as "Hul praat met hom.", though the latter is more informal.
  2. The formal, u (pronounced as [œ]), functions like a plural, but refers to both singular and plural. This form is used to show respect and is used toward one's superiors (a boss or teacher, for instance), to a stranger, to older people or to the Christian God. When in reference to the Christian God, it is capitalized as U.

B. Object Pronouns (Oblique Case)

Person English Afrikaans English Afrikaans English Afrikaans
Singular Plural Formal
1st Pers.
me
my
us
ons
2nd Pers.
you
jou
you
julle
you
u
3rd Pers.
him
her
it
hom
haar
dit
them
hulle

The object of a sentence describes who/what the action is directed towards. Unlike German or Russian, Afrikaans, like English, does not distinguish between the Direct Object (Accusative Case) and Indirect Object (Dative Case). Thus, all objective pronouns remain the same.

  • 'I know him.' → "Ek ken hom."

It should be noted that every plural object pronoun (including u) is the exact same as its subject form.

  • 'She forgets you.' → "Sy vergeet u."
  • 'He understands them.' → "Hy verstaan hulle/hul."

IV. Practicality: Greetings and Phrases

Afrikaans greetings are used in the exact same contexts as English ones, though with more attention to formality. When in an informal context, you might greet someone with a "haai" rather than a "hallo" or a "goeiedag". For instance, goeienaand is used when greeting a person during the evening while goeienag is used when leaving; No different from English.

A small thing to note is that the 'Good [x]' forms below exist as one word when posed as an interjection/greeting ('good afternoon!' = "Goeiemiddag!"), but the form becomes two words when talking about a good part of the day ('it was a good afternoon' = "Dit was ʼn goeie middag.").

English Afrikaans Notes
hello hallo
hi haai
goodbye totsiens Literally a compound of tot (till) + sien (to see)
good day goeiedag A compound of goed (good) + dag (day)
good morning goeiemôre A compound of goed (good) + môre (morrow, morning)
good afternoon goeiemiddag A compound of goed (good) + middag (midday, afternoon)
good evening goeienaand A compound of goed (good) + aand (evening). Note the extra n in goeienaand.
goodnight goeienag A compound of goed (good) + nag (night)
How are you? Hoe gaan dit (met jou/u/julle)? Though this phrase can be shortened informally to "Hoe gaan dit?", the phrase in full is "Hoe gaan dit met jou/u/julle?", this dependent on person and formality.
I'm fine Dit gaan goed (met my) The phrase is a direct answer to "Hoe gaan dit?", the ending depending on formality again.
My name is... My naam is...
(many) thanks (baie) dankie
please asseblief
pleased to meet you aangename kennis The phrase is literally translated as aangenaam (pleasant) + kennis (knowledge)

In later lessons, the different given forms in the notes will be expounded on and will make sense to the learner (eg. Why Good becomes Goeie). For now, just learn the forms as given.

V. Verbs: The Infinitive, Present Simple and Present Continuous

The Infinitive

The infinitive, sometimes referred to as the verb's 'dictionary form', is formed in English by adding 'to' before the verb's present participle. The infinitive is the form of a verb without a subject or specific tense.

  • to walk, to sleep, to eat.

In Afrikaans, the infinitive form is formed by adding 'om te' before the participle.

  • om te loop, om te slaap, om te eet.

The Present Simple and Present Continuous

Fortunately, Afrikaans has extremely simple conjugation. If you look at every present form in every countable person, you will notice that the verb and its participle NEVER change. There is no direct distinction between verb forms of the present simple or present continuous.

  • "Ek eet ʼn appel." → 'I eat an apple' or 'I am eating an apple.'
  • "Ek slaap in die bed." → 'I sleep in the bed.' or 'I am sleeping in the bed.'

However, it must be noted that there are literal ways to describe the continuous, and we shall cover it in future lessons. Another thing to know is that there are two very common verbs that deviate completely from the conjugation's common ruleset: "om te wees" ('to be') and "om te hê" ('to have'), which we'll cover in the next lesson.

Person English Afrikaans English Afrikaans
Present Simple Present Continuous
Singular
1st Pers.
I walk
ek loop
I am walking
ek loop
2nd Pers.
you walk
jy/u loop
you are walking
jy/u loop
3rd Pers.
he/she/it walks
hy/sy/dit loop
he/she/it is walking
hy/sy/dit loop
Present Simple Present Continuous
Plural
1st Pers.
we walk
ons loop
we are walking
ons loop
2nd Pers.
you walk
julle loop
you are walking
julle loop
3rd Pers.
they walk
hulle loop
they are walking
hulle loop

VI. Chapter Vocabulary

This is the chapter's main vocabulary, common ones that will appear in the dialogue section and following exercises. Still, one should take note of the example words used in the grammatical explanations and try to keep them in mind, as they will appear in the exercises too.

English Afrikaans English Afrikaans English Afrikaans
Numerals: 0 - 10 Nouns, Adjectives & Conjunctions Verbs and Adverbs
one een also ook to be (pres. am/are/is) om te wees (pres. is)
two twee and en to eat om te eet
three drie boss baas to have om te hê (pres. het)
four vier food kos to live, to reside om te woon
five vyf madam mevrou to see om te sien
six ses mister; sir meneer to sleep om te slaap
seven sewe night nag to think om te dink
eight agt pretty mooi yes ja
nine nege river rivier no nee
ten tien store winkel very; many; much baie
today vandag
weather weer
woman vrou

VII. Chapter Dialogues

Each lesson, two different dialogues related to the material of the lesson is provided to get the learner familiar with the material at hand. Having reviewed this lesson's notes, you should be able to understand the grammatical structure. If you must look at the vocabulary above or translation below, do so sparingly.

Dialogue 1: An Informal Conversation

Sonja Goeiemôre, Johan!
Johan Haai, Sonja! Hoe gaan dit?
Sonja Dit gaan goed, dankie. En met jou?
Johan Ook goed. Die weer is goed vandag, né?
Sonja Ja, ek dink so.
Translation
Sonja Good morning, Johan!
Johan Hi, Sonja! How are you?
Sonja I'm fine, thanks. And you?
Johan Also well. The weather is good today, huh?
Sonja Yes, I think so.

Dialogue 2: A Formal Conversation

Die Baas Goeiedag, Johan.
Johan Goeiemôre, meneer. Hoe gaan dit met u?
Die Baas Dit gaan goed met my, dankie. Waar is Japie?
Johan Hy is besig in die winkel.
Die Baas Baie dankie, Johan. Totsiens.
Johan Totsiens, meneer.
Translation
The Boss Good day, Johan.
Johan Good morning, sir. How are you?
The Boss I'm fine, thanks. Where is Japie?
Johan He is busy in the store.
The Boss Thank you very much, Johan. Goodbye
Johan Goodbye, sir.

Exercises

Exercise A: Translate into English:

Translate these sentences into English.

  • Goeienaand en goeienag.
  • Die dag is sonnig.
  • Die woud is mooi in die somer.
  • My naam is Japie, en hier is my vriend, Valerie.
  • Hul werk op ʼn skip.
  • Waar is my ander skoen?
  • Een, Vyf, Nege, Ses, Sewe, Twee
ANSWER(S)
  • Good evening and goodnight.
  • The day is sunny.
  • The forest is pretty in the summer.
  • My name is Japie, and here is my friend, Valerie.
  • They work on a ship.
  • Where is my other shoe?
  • One, Five, Nine, Six, Seven, Two

Exercise B: Translate into Afrikaans:

Translate these sentences into Afrikaans.

  • Hello, my name is Sally. Pleased to meet you.
  • The river is icy in the winter.
  • The madam lives here.
  • You (plural) eat an apple.
  • We are sleeping.
  • Hi! Where is the boss?
  • You (formal) see him.
ANTWOORD(E)
  • Hallo, my naam is Sally. Aangename kennis.
  • Die rivier is ysig in die winter.
  • Die mevrou woon hier.
  • Julle eet ʼn appel.
  • Ons slaap.
  • Haai! Waar is die baas?
  • U sien hom.

The Next Lesson

In the next lesson, we shall cover months and seasons, plurals, the past tense, "om te wees" and "om te hê" and possessive pronouns. Good luck on your studies!
On to Lesson Two!>>


Lesson Two

Afrikaans Les Twee: Descriptions

Definite and Indefinite Articles

Gender

Many languages will give words grammatical gender, but this is not the case for Afrikaans, just like English, there is no gender and thus nouns have no classification.

The

In English we use the word "the" to point out a specific thing. If someone says, "I ate all of the cake", they aren't referring to any cake, it's a specific one. Afrikaans has the same thing. In Afrikaans this word is "die", and just like in English, it can be used for the singular and the plural.

English: the dogs, the tree, the walls

Afrikaans: die honde, die boom, die mure.

A/An

The Afrikaans word for "a" or "an" is " 'n". This is called the indefinite article because it means one thing, but it cannot refer to a specific thing such as in the sentence "I ate a cake". This could be any cake. 'n Is always written with an apostrophe (') and is never capitalized, even if it starts a sentence. If it starts a sentence, then the first letter of the following word gets capitalized.

Forming Questions

There are two main ways of forming question words: by starting out with a question word (What language are you learning?) or by turning a statement into a question (You are learning Afrikaans becomes Are you learning Afrikaans?).

Question Words

English Afrikaans
what wat
who wie
whose wie se
why hoekom / waarom
where waar
when wanneer
which watter
how hoe
how much/many hoeveel

When making simple sentences, these questions will have question word-verb-object word order.

  • English: Who is the president of South Africa?
  • Afrikaans: Wie is die president van Suid-Afrika?
  • English: Where do you live?
  • Afrikaans: Waar woon jy?

Questions Beginning with Verbs

Often we ask questions that don't start with question words, but with verbs. Afrikaans does this too. The difference in word order: in English we say "Do you write letters?" but in Afrikaans it would read "Write you letters?". The verb comes first, followed by the subject, than the object. It is important to remember however that word order will change when we add more complex elements.

  • English: Do you smoke cigars?
  • Afrikaans: Rook julle sigare?

Adjectives

When adjectives are used with the verb wees ("She is sick", "He is blonde") you can use the form of the adjective you'll find in the dictionary. However, when an adjective is directly modifying a noun (as in "She is a sick girl", "He has blonde hair") their form usually alter somewhat. This change is called inflection. As a general rule, polysyllabic adjectives are normally inflected; monosyllabic adjectives may or may not be inflected though, depending mostly on a set of rather complex phonological rules. When an adjective is inflected, it usually takes the ending -e and a series of morphological changes may result. For example, the final t following an /x/ sound, which disappears in uninflected adjectives like reg, is restored when the adjective is inflected (regte). A similar phenomenon applies to the addition of t after /s/. For example, the adjective vas becomes vaste when inflected. Conversely, adjectives ending in -d (pronounced /t/) or -g (pronounced /x/) following a long vowel or diphthong, lose the -d and -g when inflected.

Adjectives come before nouns, like in English.

English Afrikaans
Uninflected Inflected
black swart swarte
fast vinnig vinnige
deaf doof dowe
cold koud koue
low laag lae
high hoog hoë
Adjectives ending in a 'g' — add a 'te'
bad sleg slegte
Adjectives ending in 'f' — change it to two 'w's
silly laf lawwe
Irregulars
good goed goeie
old oud ou, oue
new nuut nuwe

Possessive Pronouns

  • "mine" – "myne"
  • "yours" (singular)- "jou" or "u" (joune?)
  • "his" – "sy"
  • "her" – "haar"
  • "our" – "ons" (onse?)
  • "yours" (plural) – "julle"
  • "their" – "hulle"

<<Back to Lesson One

On to Lesson Three!>>


Lesson Three

Afrikaans Les Drie: Nommers

Number Afrikaans English
0 Nul Zero
1 Een One
2 Twee Two
3 Drie Three
4 Vier Four
5 Vyf Five
6 Ses Six
7 Sewe Seven
8 Agt Eight
9 Nege Nine
10 Tien Ten
11 Elf Eleven
12 Twaalf Twelve
13 Dertien Thirteen
14 Veertien Fourteen
15 Vyftien Fifteen
16 Sestien Sixteen
17 Sewentien Seventeen
18 Agtien Eighteen
19 Negentien Nineteen
20 Twintig Twenty

With this knowledge, you can count up to twenty.

30 Dertig Thirty
40 Veertig Forty
50 Vyftig Fifty
60 Sestig Sixty
70 Sewentig Seventy
80 Tagtig Eighty
90 Negentig Ninety
100 Eenhonderd One hundred

To find other numbers, the format is <ONES> en <TENS>. Replace <ONES> with a number between one and nine. Replace <TENS> with twintig, dertig, veertig, vyftig, sestig, sewentig, tagtig, or negentig. For example, een en twintig translates to twenty one. Now you can count up to ninety nine!


<<Back to Lesson Two

On to Lesson Four!>>


External Links

Afrikaans/External Links


Newspapers

Here is a list of newspapers in South Africa and Namibia.

  Suid-Afrikaanse koerante (Afrikaans), South African newspapers

  Namibiese koerante (Afrikaans), Namibian newspapers



Contributors

The Afrikaans Language textbook was first started on June 12, 2005. Add yourself to the list below if you feel you've made a significant contribution to this textbook.


GNU FREE DOCUMENTATION LICENSE

Version 1.3, 3 November 2008 Copyright (C) 2000, 2001, 2002, 2007, 2008 Free Software Foundation, Inc. <http://fsf.org/>

Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed.

0. PREAMBLE

The purpose of this License is to make a manual, textbook, or other functional and useful document "free" in the sense of freedom: to assure everyone the effective freedom to copy and redistribute it, with or without modifying it, either commercially or noncommercially. Secondarily, this License preserves for the author and publisher a way to get credit for their work, while not being considered responsible for modifications made by others.

This License is a kind of "copyleft", which means that derivative works of the document must themselves be free in the same sense. It complements the GNU General Public License, which is a copyleft license designed for free software.

We have designed this License in order to use it for manuals for free software, because free software needs free documentation: a free program should come with manuals providing the same freedoms that the software does. But this License is not limited to software manuals; it can be used for any textual work, regardless of subject matter or whether it is published as a printed book. We recommend this License principally for works whose purpose is instruction or reference.

1. APPLICABILITY AND DEFINITIONS

This License applies to any manual or other work, in any medium, that contains a notice placed by the copyright holder saying it can be distributed under the terms of this License. Such a notice grants a world-wide, royalty-free license, unlimited in duration, to use that work under the conditions stated herein. The "Document", below, refers to any such manual or work. Any member of the public is a licensee, and is addressed as "you". You accept the license if you copy, modify or distribute the work in a way requiring permission under copyright law.

A "Modified Version" of the Document means any work containing the Document or a portion of it, either copied verbatim, or with modifications and/or translated into another language.

A "Secondary Section" is a named appendix or a front-matter section of the Document that deals exclusively with the relationship of the publishers or authors of the Document to the Document's overall subject (or to related matters) and contains nothing that could fall directly within that overall subject. (Thus, if the Document is in part a textbook of mathematics, a Secondary Section may not explain any mathematics.) The relationship could be a matter of historical connection with the subject or with related matters, or of legal, commercial, philosophical, ethical or political position regarding them.

The "Invariant Sections" are certain Secondary Sections whose titles are designated, as being those of Invariant Sections, in the notice that says that the Document is released under this License. If a section does not fit the above definition of Secondary then it is not allowed to be designated as Invariant. The Document may contain zero Invariant Sections. If the Document does not identify any Invariant Sections then there are none.

The "Cover Texts" are certain short passages of text that are listed, as Front-Cover Texts or Back-Cover Texts, in the notice that says that the Document is released under this License. A Front-Cover Text may be at most 5 words, and a Back-Cover Text may be at most 25 words.

A "Transparent" copy of the Document means a machine-readable copy, represented in a format whose specification is available to the general public, that is suitable for revising the document straightforwardly with generic text editors or (for images composed of pixels) generic paint programs or (for drawings) some widely available drawing editor, and that is suitable for input to text formatters or for automatic translation to a variety of formats suitable for input to text formatters. A copy made in an otherwise Transparent file format whose markup, or absence of markup, has been arranged to thwart or discourage subsequent modification by readers is not Transparent. An image format is not Transparent if used for any substantial amount of text. A copy that is not "Transparent" is called "Opaque".

Examples of suitable formats for Transparent copies include plain ASCII without markup, Texinfo input format, LaTeX input format, SGML or XML using a publicly available DTD, and standard-conforming simple HTML, PostScript or PDF designed for human modification. Examples of transparent image formats include PNG, XCF and JPG. Opaque formats include proprietary formats that can be read and edited only by proprietary word processors, SGML or XML for which the DTD and/or processing tools are not generally available, and the machine-generated HTML, PostScript or PDF produced by some word processors for output purposes only.

The "Title Page" means, for a printed book, the title page itself, plus such following pages as are needed to hold, legibly, the material this License requires to appear in the title page. For works in formats which do not have any title page as such, "Title Page" means the text near the most prominent appearance of the work's title, preceding the beginning of the body of the text.

The "publisher" means any person or entity that distributes copies of the Document to the public.

A section "Entitled XYZ" means a named subunit of the Document whose title either is precisely XYZ or contains XYZ in parentheses following text that translates XYZ in another language. (Here XYZ stands for a specific section name mentioned below, such as "Acknowledgements", "Dedications", "Endorsements", or "History".) To "Preserve the Title" of such a section when you modify the Document means that it remains a section "Entitled XYZ" according to this definition.

The Document may include Warranty Disclaimers next to the notice which states that this License applies to the Document. These Warranty Disclaimers are considered to be included by reference in this License, but only as regards disclaiming warranties: any other implication that these Warranty Disclaimers may have is void and has no effect on the meaning of this License.

2. VERBATIM COPYING

You may copy and distribute the Document in any medium, either commercially or noncommercially, provided that this License, the copyright notices, and the license notice saying this License applies to the Document are reproduced in all copies, and that you add no other conditions whatsoever to those of this License. You may not use technical measures to obstruct or control the reading or further copying of the copies you make or distribute. However, you may accept compensation in exchange for copies. If you distribute a large enough number of copies you must also follow the conditions in section 3.

You may also lend copies, under the same conditions stated above, and you may publicly display copies.

3. COPYING IN QUANTITY

If you publish printed copies (or copies in media that commonly have printed covers) of the Document, numbering more than 100, and the Document's license notice requires Cover Texts, you must enclose the copies in covers that carry, clearly and legibly, all these Cover Texts: Front-Cover Texts on the front cover, and Back-Cover Texts on the back cover. Both covers must also clearly and legibly identify you as the publisher of these copies. The front cover must present the full title with all words of the title equally prominent and visible. You may add other material on the covers in addition. Copying with changes limited to the covers, as long as they preserve the title of the Document and satisfy these conditions, can be treated as verbatim copying in other respects.

If the required texts for either cover are too voluminous to fit legibly, you should put the first ones listed (as many as fit reasonably) on the actual cover, and continue the rest onto adjacent pages.

If you publish or distribute Opaque copies of the Document numbering more than 100, you must either include a machine-readable Transparent copy along with each Opaque copy, or state in or with each Opaque copy a computer-network location from which the general network-using public has access to download using public-standard network protocols a complete Transparent copy of the Document, free of added material. If you use the latter option, you must take reasonably prudent steps, when you begin distribution of Opaque copies in quantity, to ensure that this Transparent copy will remain thus accessible at the stated location until at least one year after the last time you distribute an Opaque copy (directly or through your agents or retailers) of that edition to the public.

It is requested, but not required, that you contact the authors of the Document well before redistributing any large number of copies, to give them a chance to provide you with an updated version of the Document.

4. MODIFICATIONS

You may copy and distribute a Modified Version of the Document under the conditions of sections 2 and 3 above, provided that you release the Modified Version under precisely this License, with the Modified Version filling the role of the Document, thus licensing distribution and modification of the Modified Version to whoever possesses a copy of it. In addition, you must do these things in the Modified Version:

  1. Use in the Title Page (and on the covers, if any) a title distinct from that of the Document, and from those of previous versions (which should, if there were any, be listed in the History section of the Document). You may use the same title as a previous version if the original publisher of that version gives permission.
  2. List on the Title Page, as authors, one or more persons or entities responsible for authorship of the modifications in the Modified Version, together with at least five of the principal authors of the Document (all of its principal authors, if it has fewer than five), unless they release you from this requirement.
  3. State on the Title page the name of the publisher of the Modified Version, as the publisher.
  4. Preserve all the copyright notices of the Document.
  5. Add an appropriate copyright notice for your modifications adjacent to the other copyright notices.
  6. Include, immediately after the copyright notices, a license notice giving the public permission to use the Modified Version under the terms of this License, in the form shown in the Addendum below.
  7. Preserve in that license notice the full lists of Invariant Sections and required Cover Texts given in the Document's license notice.
  8. Include an unaltered copy of this License.
  9. Preserve the section Entitled "History", Preserve its Title, and add to it an item stating at least the title, year, new authors, and publisher of the Modified Version as given on the Title Page. If there is no section Entitled "History" in the Document, create one stating the title, year, authors, and publisher of the Document as given on its Title Page, then add an item describing the Modified Version as stated in the previous sentence.
  10. Preserve the network location, if any, given in the Document for public access to a Transparent copy of the Document, and likewise the network locations given in the Document for previous versions it was based on. These may be placed in the "History" section. You may omit a network location for a work that was published at least four years before the Document itself, or if the original publisher of the version it refers to gives permission.
  11. For any section Entitled "Acknowledgements" or "Dedications", Preserve the Title of the section, and preserve in the section all the substance and tone of each of the contributor acknowledgements and/or dedications given therein.
  12. Preserve all the Invariant Sections of the Document, unaltered in their text and in their titles. Section numbers or the equivalent are not considered part of the section titles.
  13. Delete any section Entitled "Endorsements". Such a section may not be included in the Modified version.
  14. Do not retitle any existing section to be Entitled "Endorsements" or to conflict in title with any Invariant Section.
  15. Preserve any Warranty Disclaimers.

If the Modified Version includes new front-matter sections or appendices that qualify as Secondary Sections and contain no material copied from the Document, you may at your option designate some or all of these sections as invariant. To do this, add their titles to the list of Invariant Sections in the Modified Version's license notice. These titles must be distinct from any other section titles.

You may add a section Entitled "Endorsements", provided it contains nothing but endorsements of your Modified Version by various parties—for example, statements of peer review or that the text has been approved by an organization as the authoritative definition of a standard.

You may add a passage of up to five words as a Front-Cover Text, and a passage of up to 25 words as a Back-Cover Text, to the end of the list of Cover Texts in the Modified Version. Only one passage of Front-Cover Text and one of Back-Cover Text may be added by (or through arrangements made by) any one entity. If the Document already includes a cover text for the same cover, previously added by you or by arrangement made by the same entity you are acting on behalf of, you may not add another; but you may replace the old one, on explicit permission from the previous publisher that added the old one.

The author(s) and publisher(s) of the Document do not by this License give permission to use their names for publicity for or to assert or imply endorsement of any Modified Version.

5. COMBINING DOCUMENTS

You may combine the Document with other documents released under this License, under the terms defined in section 4 above for modified versions, provided that you include in the combination all of the Invariant Sections of all of the original documents, unmodified, and list them all as Invariant Sections of your combined work in its license notice, and that you preserve all their Warranty Disclaimers.

The combined work need only contain one copy of this License, and multiple identical Invariant Sections may be replaced with a single copy. If there are multiple Invariant Sections with the same name but different contents, make the title of each such section unique by adding at the end of it, in parentheses, the name of the original author or publisher of that section if known, or else a unique number. Make the same adjustment to the section titles in the list of Invariant Sections in the license notice of the combined work.

In the combination, you must combine any sections Entitled "History" in the various original documents, forming one section Entitled "History"; likewise combine any sections Entitled "Acknowledgements", and any sections Entitled "Dedications". You must delete all sections Entitled "Endorsements".

6. COLLECTIONS OF DOCUMENTS

You may make a collection consisting of the Document and other documents released under this License, and replace the individual copies of this License in the various documents with a single copy that is included in the collection, provided that you follow the rules of this License for verbatim copying of each of the documents in all other respects.

You may extract a single document from such a collection, and distribute it individually under this License, provided you insert a copy of this License into the extracted document, and follow this License in all other respects regarding verbatim copying of that document.

7. AGGREGATION WITH INDEPENDENT WORKS

A compilation of the Document or its derivatives with other separate and independent documents or works, in or on a volume of a storage or distribution medium, is called an "aggregate" if the copyright resulting from the compilation is not used to limit the legal rights of the compilation's users beyond what the individual works permit. When the Document is included in an aggregate, this License does not apply to the other works in the aggregate which are not themselves derivative works of the Document.

If the Cover Text requirement of section 3 is applicable to these copies of the Document, then if the Document is less than one half of the entire aggregate, the Document's Cover Texts may be placed on covers that bracket the Document within the aggregate, or the electronic equivalent of covers if the Document is in electronic form. Otherwise they must appear on printed covers that bracket the whole aggregate.

8. TRANSLATION

Translation is considered a kind of modification, so you may distribute translations of the Document under the terms of section 4. Replacing Invariant Sections with translations requires special permission from their copyright holders, but you may include translations of some or all Invariant Sections in addition to the original versions of these Invariant Sections. You may include a translation of this License, and all the license notices in the Document, and any Warranty Disclaimers, provided that you also include the original English version of this License and the original versions of those notices and disclaimers. In case of a disagreement between the translation and the original version of this License or a notice or disclaimer, the original version will prevail.

If a section in the Document is Entitled "Acknowledgements", "Dedications", or "History", the requirement (section 4) to Preserve its Title (section 1) will typically require changing the actual title.

9. TERMINATION

You may not copy, modify, sublicense, or distribute the Document except as expressly provided under this License. Any attempt otherwise to copy, modify, sublicense, or distribute it is void, and will automatically terminate your rights under this License.

However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation.

Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice.

Termination of your rights under this section does not terminate the licenses of parties who have received copies or rights from you under this License. If your rights have been terminated and not permanently reinstated, receipt of a copy of some or all of the same material does not give you any rights to use it.

10. FUTURE REVISIONS OF THIS LICENSE

The Free Software Foundation may publish new, revised versions of the GNU Free Documentation License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. See http://www.gnu.org/copyleft/.

Each version of the License is given a distinguishing version number. If the Document specifies that a particular numbered version of this License "or any later version" applies to it, you have the option of following the terms and conditions either of that specified version or of any later version that has been published (not as a draft) by the Free Software Foundation. If the Document does not specify a version number of this License, you may choose any version ever published (not as a draft) by the Free Software Foundation. If the Document specifies that a proxy can decide which future versions of this License can be used, that proxy's public statement of acceptance of a version permanently authorizes you to choose that version for the Document.

11. RELICENSING

"Massive Multiauthor Collaboration Site" (or "MMC Site") means any World Wide Web server that publishes copyrightable works and also provides prominent facilities for anybody to edit those works. A public wiki that anybody can edit is an example of such a server. A "Massive Multiauthor Collaboration" (or "MMC") contained in the site means any set of copyrightable works thus published on the MMC site.

"CC-BY-SA" means the Creative Commons Attribution-Share Alike 3.0 license published by Creative Commons Corporation, a not-for-profit corporation with a principal place of business in San Francisco, California, as well as future copyleft versions of that license published by that same organization.

"Incorporate" means to publish or republish a Document, in whole or in part, as part of another Document.

An MMC is "eligible for relicensing" if it is licensed under this License, and if all works that were first published under this License somewhere other than this MMC, and subsequently incorporated in whole or in part into the MMC, (1) had no cover texts or invariant sections, and (2) were thus incorporated prior to November 1, 2008.

The operator of an MMC Site may republish an MMC contained in the site under CC-BY-SA on the same site at any time before August 1, 2009, provided the MMC is eligible for relicensing.

How to use this License for your documents

To use this License in a document you have written, include a copy of the License in the document and put the following copyright and license notices just after the title page:

Copyright (c) YEAR YOUR NAME.
Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.3
or any later version published by the Free Software Foundation;
with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
A copy of the license is included in the section entitled "GNU
Free Documentation License".

If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts, replace the "with...Texts." line with this:

with the Invariant Sections being LIST THEIR TITLES, with the
Front-Cover Texts being LIST, and with the Back-Cover Texts being LIST.

If you have Invariant Sections without Cover Texts, or some other combination of the three, merge those two alternatives to suit the situation.

If your document contains nontrivial examples of program code, we recommend releasing these examples in parallel under your choice of free software license, such as the GNU General Public License, to permit their use in free software.