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Preface to the Second EditionHow to Read This Book Chapter 1 Introduction1£®1 SimpliciaIHomology1£®2 Categories and Functors1£®3 Singular HomologyChapter 2 Hom and Tensor2£®1 Modules2£®2 Tensor Products2£®2£®1 AdjointlsomorphismsChapter 3 Special Modules3£®1 Projective Modules3£®2 InjectiveModules3£®3 Flat Modules3£®3£®1 PurityChapter 4 Specific Rings4£®1 Semisimple Rings4£®2 von Neumann Regular Rings4£®3 Hereditary and Dedekind Rings4£®4 Semihereditary and Prufer Rings4£®5 Quasi-Frobenius Rings4£®6 Semiperfect Rings4£®7 Localization4£®8 Polynomial RingsChapter 5 Setting the Stage5£®1 Categorical Constructions5£®2 Limits5£®3 Adjoint Functor Theorem for Modules5£®4 Sheaves5£®4£®1 Manifolds5£®4£®2 Sheaf Constructions5£®5 Abelian Categories5£®5£®1 ComplexesChapter 6 Homology6£®1 Homology Functors6£®2 Derived Functors6£®2£®1 Left Derived Functors6£®2£®2 Axioms6£®2£®3 Covariant Right Derived Functors6£®2£®4 Contravariant Right Derived Functors6£®3 Sheaf Cohomology6£®3£®1 Cech Cohomology6£®3£®2 Riemann-Roch TheoremChapter 7 Tor and Ext7£®1 Tor7£®1£®1 Domains7£®1£®2 Localization7£®2 Ext7£®2£®1 Baer Sum7£®3 Cotorsion Groups7£®4 Universal CoefficientsChapter 8 Homology and Rings8£®1 Dimensions ofRings8£®2 Hilbert's Syzygy Theorem8£®3 Stably Free Modules8£®4 Commutative Noetherian Local RingsChapter 9 Homology and Groups9£®1 Group Extensions9£®1£®1 Semidirect Products9£®1£®2 General Extensions and Cohomology9£®1£®3 Stabilizing Automorphisms9£®2 Group Cohomology9£®3 Bar Resolutions9£®4 Group Homology9£®4£®1 Schur Multiplier9£®5 Change of Groups9£®5£®1 Restriction and Inflation9£®6 Transfer9£®7 Tate Groups9£®8 Outer Automorphisms of p-Groups9£®9 Cohomological Dimension9£®10 Division Rings and Brauer GroupsChapter 10 Spectral Sequences10£®1 Bicomplexes10£®2 Filtrations and Exact Couples10£®3 Convergence10£®4 Homology of the Total Complex10£®5 Cartan-Eilenberg Resolutions10£®6 Grothendieck Spectral Sequences10£®7 Groups10£®8 Rings10£®9 Sheaves10£®10 Kunneth TheoremsReferencesSpecial NotationIndex