This book provides a self-contained systematic treatment of the subject of relative homological algebra. It is designed for graduate students as well as researchers and specialists. It contains twelve chapters with abundant supply of important results with complete proofs covering material that is essential to understanding topics in algebra, algebraic geometry, and algebraic topology. The text also contains results that are in book form for the first time and thus provides essential reading for researchers and specialists. At the end of each section of each chapter, there are exercises that provide practice problems for students as well as additional important results for specialists.

The book can be used as a text for graduate students and as a handbook for researchers and specialists. The material in the first three chapters constitute notes from lectures of the authors at their respective universities and is suitable for an introductory course in module and ring theory. The following chapters are suitable for a course in relative homological algebra and its applications to commutative and non-commutative algebra. The last three chapters give applications to ring theory. These chapters together with Chapter 7 contain recent achievements including a solution to the flat cover conjecture.