As it says on the front cover this book is an introduction to Category Theory. It gives the basic definitions; goes through the various associated gadgetry such as functors, natural transformations, limits and colimits; and then explains adjunctions. This material could be developed in 50 pages or so, but here it takes some 220 pages. That is because there are many examples illustrating the various notions, some rather straightforward, and others with more content. More importantly, there are also over 200 exercises. And perhaps even more importantly, solutions to these exercises are available online.

The book is aimed primarily at the beginning graduate student, but that does not mean that other students or professional mathematicians will not find it useful. I have designed the book so that it can be used by a single student or small group of students to learn the subject on their own. The book will make a suitable text for a reading group. The book does not assume the reader has a broad knowledge of mathematics. Most of the illustrations use rather simple ideas, but every now and then a more advanced topic is mentioned. The book can also be used as a recommended text for a taught introductory course.

Every mathematician should at least know of the existence of category theory, and many will need to use categorical notions every now and then. For those groups this is the book you should have. Other mathematicians will use category theory every day.