`xy` is a special package for drawing diagrams. To use it, simply add the following line to the preamble of your document:

```
\usepackage[all]{xy}
```

where "all" means you want to load a large standard set of functions from *Xy-pic*, suitable for developing the kind of diagrams discussed here.

The primary way to draw *Xy-pic* diagrams is over a matrix-oriented canvas, where each diagram element is placed in a matrix slot:

```
\begin{displaymath}
\xymatrix{A & B \\
C & D }
\end{displaymath}
``` |

The `\xymatrix` command must be used in math mode. Here, we specified two lines and two columns. To make this matrix a diagram we just add directed arrows using the `\ar` command.

```
\begin{displaymath}
\xymatrix{ A \ar[r] & B \ar[d] \\
D \ar[u] & C \ar[l] }
\end{displaymath}
``` |

The arrow command is placed on the origin cell for the arrow. The arguments are the direction the arrow should point to (up, down, right and left).

```
\begin{displaymath}
\xymatrix{
A \ar[d] \ar[dr] \ar[r] & B \\
D & C }
\end{displaymath}
``` |

To make diagonals, just use more than one direction. In fact, you can repeat directions to make bigger arrows.

```
\begin{displaymath}
\xymatrix{
A \ar[d] \ar[dr] \ar[drr] & & \\
B & C & D }
\end{displaymath}
``` |

We can draw even more interesting diagrams by adding labels to the arrows. To do this, we use the common superscript and subscript operators.

```
\begin{displaymath}
\xymatrix{
A \ar[r]^f \ar[d]_g & B \ar[d]^{g'} \\
D \ar[r]_{f'} & C }
\end{displaymath}
``` |

As shown, you use these operators as in math mode. The only difference is that that superscript means "on top of the arrow", and subscript means "under the arrow". There is a third operator, the vertical bar: | It causes text to be placed in the arrow.

```
\begin{displaymath}
\xymatrix{
A \ar[r]|f \ar[d]|g & B \ar[d]|{g'} \\
D \ar[r]|{f'} & C }
\end{displaymath}
``` |

To draw an arrow with a hole in it, use `\ar[...]|\hole`. In some situations, it is important to distinguish between different types of arrows. This can be done by putting labels on them, or changing their appearance

```
\begin{displaymath}
\xymatrix{
\bullet\ar@{->}[rr] && \bullet\\
\bullet\ar@{.<}[rr] && \bullet\\
\bullet\ar@{~)}[rr] && \bullet\\
\bullet\ar@{=(}[rr] && \bullet\\
\bullet\ar@{~/}[rr] && \bullet\\
\bullet\ar@{^{(}->}[rr] && \bullet\\
\bullet\ar@2{->}[rr] && \bullet\\
\bullet\ar@3{->}[rr] && \bullet\\
\bullet\ar@{=+}[rr] && \bullet }
\end{displaymath}
``` |

Notice the difference between the following two diagrams:

```
\begin{displaymath}
\xymatrix{ \bullet \ar[r] \ar@{.>}[r] & \bullet }
\end{displaymath}
``` |

```
\begin{displaymath}
\xymatrix{
\bullet \ar@/^/[r]
\ar@/_/@{.>}[r] &
\bullet }
\end{displaymath}
``` |

The modifiers between the slashes define how the curves are drawn. *Xy-pic* offers many ways to influence the drawing of curves; for more information, check the *Xy-pic* documentation.

If you are interested in a more thorough introduction then consult the Xy-pic Home Page, which contains links to several other tutorials as well as the reference documentation.