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MODULES Modules Free Modules Exact Sequences Homomorphisms Tensor Product of Modules Direct and Inverse Limits Pull Back and Push Out CATEGORIES AND FUNCTORS Categories Functors The Functors Hom and Tensor PROJECTIVE AND INJECTIVE MODULES Projective Modules Injective Modules Baer's Criterion An Embedding Theorem HOMOLOGY OF COMPLEXES Ker-Coker Sequence Connecting Homomorphism: The General Case Homotopy DERIVED FUNCTORS Projective Resolutions Injective Resolutions Derived Functors TORSION AND EXTENSION FUNCTORS Derived Functors--Revisited Torsion and Extension Functors Some Further Properties of Torsion Functors Tor and Direct Limits THE FUNCTOR ExtnR Ext1 and Extensions Baer Sum of Extensions Some Further Properties of Extension Functors HEREDITARY AND SEMIHEREDITARY RINGS Hereditary Rings and Dedekind Domains Invertible Ideals and Dedekind Rings Semihereditary and Prufer Rings UNIVERSAL COEFFICIENT THEOREM Universal Coefficient Theorem for Homology Universal Coefficient Theorem for Cohomology The Kunneth Formula: A Special Case DIMENSIONS OF MODULES AND RINGS Projectively and Injectively Equivalent Modules Dimensions of Modules and Rings Global Dimension of Rings Global Dimension of Noetherian Rings Global Dimension of Artin Rings COHOMOLOGY OF GROUPS Homology and Cohomology Groups Some Examples The Groups H0(G,A) and H0(G,A) The Groups H1(G,A) and H1(G,A) Homology and Cohomology of Direct Sums The Bar Resolution Second Cohomology Group and Extensions Some Homomorphisms Some Exact Sequences SOME APPLICATIONS An Exact Sequence Outer Automorphisms of p-Groups A Theorem of Magnus BIBLIOGRAPHY INDEX