Chapter l Simplicial sets 1．Basic definitions 2．Realization 3．Kan complexes 4．Anodyne extensions 5．Function complexes 6．Simplicial homotopy 7．Simplicial homotopy groups 8．Fundamental groupoid 9．Categories of fibrant objects 10．Minimal fibrations 11．The closed model structure Chapter II Model Categories 1．Homotopical algebra 2．Simplicial categories 3．Simplicial model categories 4．The existence of simplicial model category structures 5．Examples of simplicial model categories 6．A generalization of Theorem 4．1 7．Quillen’S total derived functor theorem 8．Homotopy cartesian diagrams Chapter III Classical results and constructions 1．The fundamental groupoid．revisited 2．Simplicial abelian groups 3．The Hurewicz map 4．The Ex∞functor 5．The Kan suspension Chapter IV Bisimplicial sets 1．Bisimplicial sets：first properties 2．Bisimplicial abelian groups 2．1．The translation object 2．2 The generalized Eilenberg-Zilber theorem 3．Closed model structures for bisimplicial sets 3．1．The Bousfield-Kan structure 3．2．The Reedy structure 3．3．The Moerdijk structure 4．The Bousfield―Friedlander theorem 5．Theorem B and group completion 5．1．The’serre spectral sequence 5．2．Theorem B 5．3．The group completion theorem Chapter V Simplicial groups 1．Skeleta 2．Principal fibrations I：simplicial G-spaces 3．Principal fibrations II：classifications 4．Universal cocycles and WG 5．The loop group construction 6．Reduced simplicial sets，Milnor’S FK-construction 7．Simplicial groupoids Chapter VI The homotopy theory of towers 1．A model category structure for towers of spaces 2．The spectral sequence of a tower of fibrations 3．Postnikov towers 4．Local coefficients and equivariant cohomology 5．On k-invariants 6．Nilpotent spaces Chapter VII Reedy model categories 1．Decomposition of simplicial objects 2．Reedy model category structures 3．Geometric realization 4．Cosimplicial spaces Chapter VIII Cosimplicial spaces：applications 1．The homotopy spectral sequence of a cosimplicial space 2．Homotopy inverse limits 3．Completions 4．Obstruction theory Chapter IX Simplicial functors and homotopy coherence 1．Simplicial functors 2．The Dwyer-Kan theorem 3．Homotopy coherence 3．1．Classical homotopy COherence 3．2．Homotopy coherence：an expanded version 3．3．Lax functors 3．4．The Grothendieck construction 4．Realization theorems Chapter X Localization 1．Localization with respect to a map 2．The closed model category structure 3．Bousfield localization． 4．A model for the stable homotopy category References Index
