Homology (Third Corrected Printing)

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.

Biography of Saunders Mac Lane

Saunders Mac Lane was born on August 4, 1909 in Connecticut. He studied at Yale University and then at the University of Chicago and at Göttingen, where he received the D.Phil. in 1934. He has tought at Harvard, Cornell and the University of Chicago.

Mac Lane's initial research was in logic and in algebraic number theory (valuation theory). With Samuel Eilenberg he published fifteen papers on algebraic topology. A number of them involved the initial steps in the cohomology of groups and in other aspects of homological algebra - as well as the discovery of category theory. His famous and undergraduate textbook Survey of modern algebra, written jointly with G. Birkhoff, has remained in print for over 50 years. Mac Lane is also the author of several other highly successful books.