Acyclic models is a method heavily used to analyze and compare various homology and cohomology theories appearing in topology and algebra. This book is the first attempt to put together in a concise form this important technique and to include all the necessary background. It presents a brief introduction to category theory and homological algebra. The author then gives the background of the theory of differential modules and chain complexes over an abelian category to state the main acyclic models theorem, generalizing and systemizing the earlier material. This is then applied to various cohomology theories in algebra and topology. The volume could be used as a text for a course that combines homological algebra and algebraic topology. Required background includes a standard course in abstract algebra and some knowledge of topology. The volume contains many exercises. It is also suitable as a reference work for researchers. Titles in this series are copublished with the Centre de Recherches Mathématiques. Readership Graduate students and research mathematicians interested in category theory and homological algebra. Reviews "I like this book. It covers ground not often explored in textbooks ... with a perspective ... complementary to the usual."  Zentralblatt MATH "This much needed book provides a clear and selfcontained account of the cotriple approach to the cohomology theory of algebraic objects. Written by one of the founders of the subject, it will prove useful both as a teaching text and reference text for researchers."  Mathematical Reviews Table of Contents  Categories
 Abelian categories and homological algebra
 Chain complexes and simplicial objects
 Triples à la mode de Kan
 The main acyclic models theorem
 CartanEilenberg Cohomology
 Other applications in algebra
 Applications in topology
 Bibliography
 Index
