Gorenstein homological algebra is an important area of mathematics, with applications in commutative and noncommutative algebra, model category theory, representation theory, and algebraic geometry. While in classical homological algebra the existence of the projective, injective and flat resolutions over arbitrary rings is well known, things are a little different when it comes to Gorenstein homological algebra. The main open problems in this area deal with the existence of the Gorenstein injective, Gorenstein projective and Gorenstein flat resolutions.

This book is suitable for mathematicians, especially graduate students with an interest in homological algebra and its applications.