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Featuring contributions from leading international experts, Abelian Groups, Rings, and Modules, and Homological Algebra presents an introduction to this newly developing field. It reviews basic results from homological and commutative algebra, considering Gorenstein rings from a homological point of view and providing examples of Iwanaga-Gorenstein rings. It develops relative homologica algebra and shows how Tate cohomology arises from the connection between Gorenstein homological algebra and usual variety. The final three chapters look at torsion-free Abelian groups, modular representations and the properties of universal enveloping algebras, and indicate directions for future research.