This classic book provides a broad introduction to homological algebra, including a comprehensive set of exercises. Since publication of the first edition homological algebra has found a large number of applications in many different fields. Today, it is a truly indispensable tool in fields ranging from finite and infinite group theory to representation theory, number theory, algebraic topology and sheaf theory. In this new edition, the authors have selected a number of different topics and describe some of the main applications and results to illustrate the range and depths of these developments. The background assumes little more than knowledge of the algebraic theories groups and of vector spaces over a field.

This volume contains research papers and survey articles written by Beno Eckmann from 1941 to 1986. The aim of the compilation is to provide a general view of the breadth of Eckmann s mathematical work. His influence was particularly strong in the development of many subfields of topology and algebra, where he repeatedly pointed out close, and often surprising, connections between them and other areas. The surveys are exemplary in terms of how they make difficult mathematical ideas easily comprehensible and accessible even to non-specialists. The topics treated here can be classified into the following, not entirely unrelated areas: algebraic topology (homotopy and homology theory), algebra, group theory and differential geometry. Beno Eckmann was Professor of Mathematics at the University of Lausanne, 1942-48, and Principal of the Institute for Mathematical Research at the ETH Zurich, 1964-84, where he was therefore an emeritus professor."

Homological algebra has found a large number of applications in many fields ranging from finite and infinite group theory to representation theory, number theory, algebraic topology and sheaf theory. In the new edition of this broad introduction to the field, the authors address a number of select topics and describe their applications, illustrating the range and depth of their developments. A comprehensive set of exercises is included.