Graduate mathematics students will find this book an easy-to-follow, step-by-step guide to the subject. Rotman's book provides a treatment of homological algebra that approaches the subject in terms of its origins in algebraic topology. In this new edition, the book has been updated and revised throughout, with new material on sheaves and cup products added. The author has also included information about homotopical algebra, also known as K-theory. Learning homological algebra is a two-stage process. First, one must learn the language of Ext and Tor. Second, one must be able to compute these concepts with spectral sequences. This work effectively combines both aspects.