This is the second revised edition of an introduction to contemporary relative homological algebra. It supplies important material essential to understand topics in algebra, algebraic geometry and algebraic topology. Each section comes with exercises providing practice problems for students as well as additional important results for specialists.

In this new edition the authors have added well-known additional material in the first three chapters, and added new material that was not available at the time the original edition was published. In particular, the major changes are the following:

The authors also have clarified some text throughout the book and updated the bibliography by adding new references.

The book is also suitable for an introductory course in commutative and ordinary homological algebra.