Preface to the Second Edition Introduction ��.Modules 1.Modules 2.The Group of Homomorphisms 3.Sums and Products 4.Free and Projective Modules 5.Projective Modules over a Principal Ideal Domain 6.Dualization, Injective Modules 7.Injective Modules over a Principal Ideal Domain 8.Cofree Modules 9.Essential Extensions ��.Categories and Functors 1.Categories 2.Functors 3.Duality 4.Natural Transformations 5.Products and Coproducts; Universal Constructions 6.Universal Constructions (Continued); Pull-backs and Push-outs 7.Adjoint Functors 8.Adjoint Functors and Universal Constructions 9.Abelian Categories 10.Projective, Injective, and Free Objects ��.Extensions of Modules 1.Extensions 2.The Functor Ext 3.Ext Using Injectives 4.Computation of some Ext-Groups 5.Two Exact Sequences 6.A Theorem of Stein-Serre for Abelian Groups 7.The Tensor Product 8.The Functor Tor ��.Derived Funetors 1.Complexes 2.The Long Exact (Co) Homology Sequence 3.Homotopy 4.Resolutions 5.Derived Functors 6.The Two Long Exact Sequences of Derived Functor 7.The Functors Extn�� Using Projectives 8.The Functors Extn�� Using Injectives 9.Extn and n-Extensions 10.Another Characterization bfDerived Functors 11.The Functor Tot��n 12.Change of Rings ��.The Kunneth Formula 1.Double Complexes 2.The Kiinneth Theorem 3.The Dual Kunneth Theorem 4.Applications of the Kunneth Formulas ��.Cohomology of Groups 1.The Group Ring 2.Definition of (Co) Homology 3.H0, H0 4.H1, H1 with Trivial Coefficient Modules 5.The Augmentation Ideal, Derivations, and the Semi-Direct Product 6.A Short Exact Sequence 7.The (Co) Homology of Finite Cyclic Groups 8.The 5-Term Exact Sequences 9.H2, Hopf's Formula, and the Lower Central Series 10.H2 and Extensions 11.Relative Projeetives and Relative Injectives 12.Reduction Theorems 13.Resolutions 14.The (Co) Homology of a Coproduct 15.The Universal Coefficient Theorem and the (Co) Homology of a Product 16.Groups and Subgroups ��.Cohomology of Lie Algebras 1.Lie Algebras and their Universal Enveloping Algebra 2.Definition of Cohomology; H0, H1 3.H2 and Extensions 4.A Resolution of the Ground Field K 5.Semi-simple Lie Algebras 6.The two Whitehead Lemmas 7.Appendix: Hilbert's Chain-of-Syzygies Theorem ��.Exact Couples and Spectral Sequences 1.Exact Couples and Spectral Sequences 2.Filtered Differential Objects 3.Finite Convergence Conditions for Filtered Chain Complexes 4.The Ladder of an Exact Couple 5.Limits 6.Rees Systems and Filtered Complexes 7.The Limit of a Rees System 8.Completions of Filtrations 9.The Grothendieck Spectral Sequence ��.Satellites and Homology I.Projective Classes of Epimorphisms 2.��-Derived Functors 3.��-Satellites 4.The Adjoint Theorem and Examples 5.Kan Extensions and Homology 6.Applications: Homology of Small Categories, Spectral Sequences ��.Some Applications and Recent Developments I.Homological Algebra and Algebraic Topology 2.Nilpotent Groups 3.Finiteness Conditions on Groups 4.Modular Representation Theory 5.Stable and Derived Categories Bibliography Index