The objective of this book is to provision the reader with a more in depth knowledge of the material covered at A-Level in mathematics. It includes a focus on the definition and proof of concepts rather than the understanding of these concepts, which the reader is assumed to be somewhat familiar with. It is organised by concept and is neither comprehensive nor syllabus specific. Instead it is intended to allow the keen student the opportunity to gain a greater understanding of the subjects covered at A-Level and hopefully perform better in the field of mathematics as a consequence. It should not therefore be used as a sole reference for examinations and many of the explanations will contain more depth than the average student is expected to reproduce in an exam.