In presenting this treatment of homological algebra, it is a pleasureto acknowledge the help and encouragement which I have had fromall sides. Homological algebra arose from many sources in
algebra andtopology. Decisive examples came from the study of group extensionsand their factor sets, a subject I learned in joint work with OTTO SCHIL-LING. A further development of homological
ideas, with a view to theirtopological applications, came in my long collaboration with SAHUELEZLENBERG; to both collaborators, especial thanks. For many yearsthe Air Force Office of Scientific
Research supported my researchprojects on various subjects now summarized here; it is a pleasure toacknowledge their lively understanding Of basic science.