"It is written in a pedagogical, at times discursive, style and is both mathematically rigorous and easy to read … The book has an extensive index and can serve as a reference for key definitions and concepts in the subject. It will serve as an easy text for an introductory course in category theory and prove particularly valuable for the student or researcher wishing to delve further into algebraic topology and homological algebra."Mathematical Reviews Clippings Category Theory now permeates most of Mathematics, large parts of theoretical Computer Science and parts of theoretical Physics. Its unifying power brings together different branches, and leads to a deeper understanding of their roots.This book is addressed to students and researchers of these fields and can be used as a text for a first course in Category Theory. It covers its basic tools, like universal properties, limits, adjoint functors and monads. These are presented in a concrete way, starting from examples and exercises taken from elementary Algebra, Lattice Theory and Topology, then developing the theory together with new exercises and applications.Applications of Category Theory form a vast and differentiated domain. This book wants to present the basic applications and a choice of more advanced ones, based on the interests of the author. References are given for applications in many other fields.