Chapter I Simplicial sets; Chapter II Model Categories; Chapter III Classical results and constructions; Chapter IV Bisimplicial sets; Chapter V Simplicial groups; Chapter VI The homotopy theory of towers; Chapter VII Reedy model categories; Chapter VIII Cosimplicial spaces: applications; Chapter IX Simplicial functors and homotopy coherence; Chapter X Localization; References; Index.
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With the development of Quillen's concept of a closed model category and, in particular, a simplicial model category, the simplicial methods have become the primary way to describe non-abelian homological algebra and to address homotopy-theoretical issues in various fields, including algebraic K-theory. This book deals with these ideas.