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This classic and much-cited book is a systematic introduction to homological algebra, starting with basic notions in abstract algebra and category theory and continuing with an up-to-date treatment of various advanced topics. Although the subject depends on the use of very general ideas, the book proceeds from the special to the general. The main ideas are introduced gradually with many examples illustrating why they are needed and what they can do. In conclusion the book treats additive functors in an abelian category relative to a proper class of exact sequences subsuming earlier results. The author has added many historical notes and also exercises which are designed both to give elementary practice in the concepts presented and to formulate additional results not included in the text.