This text and reference book on category theory, a branch of abstract algebra, is aimed not only at students of mathematics, but also researchers and students of computer science, logic, linguistics, cognitive science, philosophy, and any of the other fields that now make use of it. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of category theory understandable to this broad readership. Although it assumes few mathematical prerequisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda's lemma; adjoints; monads. An extra topic of cartesian closed categories and the lambda-calculus is also provided; a must for computer scientists, logicians and linguists!