In presenting this treatment of homological algebra, it is a pleasure to
acknowledge the help and encouragement which I have had from all sides.
Homological algebra arose from many sources in algebra and topology.
Decisive examples came from the study of group extensions and their
factor sets, a subject I learned in joint work with OTTO SCHIL- LING. A
further development of homological ideas, with a view to their
topological applications, came in my long collaboration with SAMUEL
ElLENBERG; to both collaborators, especial thanks. For many years the
Air Force Office of Scientific Research supported my research projects
on various subjects now summarized here; it is a pleasure to acknowledge
their lively understanding of basic science. Both REINHOLD BAER and
JOSEF SCHMID read and commented on my entire manuscript; their advice
has led to many improvements. ANDERS KOCK and JACQUES RIGUET have read
the entire galley proof and caught many slips and obscurities. Among the
others whose sug- gestions have served me well, I note FRANK ADAMS,
LOUIS AUSLANDER, WILFRED COCKCROFT, ALBRECHT DOLD, GEOFFREY HORROCKS,
FRIED- RICH KASCH, JOHANN LEICHT, ARUNAS LIULEVICIUS, JOHN MOORE, DIE-
TER PUPPE, JOSEPH YAO, and a number of my current students at the
University of Chicago - not to m ntion the auditors of my lectures at
Chicago, Heidelberg, Bonn, Frankfurt, and Aarhus. My wife, DOROTHY, has
cheerfully typed more versions of more chapters than she would like to
count. Messrs.
