Preface -- Preface to the Second Edition -- 1 Basic Concepts -- 1.1 Zorn's Lemma, Ordinal and Cardinal Numbers -- 1.2 Modules -- 1.3 Tensor Products of Modules and Nakayama Lemma -- 1.4 Categories and Functors -- 1.5 Complexes of Modules and Homology -- 1.6 Direct and Inverse Limits -- 1.7 I-adic Topology and Completions -- 2 Flat Modules, Chain Conditions and Prime Ideals -- 2.1 Flat Modules -- 2.2 Localization -- 2.3 Chain Conditions -- 2.4 Prime Ideals and Primary Decomposition -- 2.5 Artin-Rees Lemma and Zariski Rings -- 3 Injective and Flat Modules -- 3.1 Injective Modules -- 3.2 Natural Identities, Flat Modules, and Injective Modules -- 3.3 Injective Modules over Commutative Noetherian Rings -- 3.4 Matlis Duality -- 4 Torsion Free Covering Modules -- 4.1 Existence of Torsion Free Precovers -- 4.2 Existence of Torsion Free Covers -- 4.3 Examples -- 4.4 Direct Sums and Products -- 5 Covers -- 5.1 ℱ-precovers and covers -- 5.2 Existence of Precovers and Covers -- 5.3 Projective and Flat Covers -- 5.4 Injective Covers -- 5.5 Direct Sums and T-nilpotency -- 6 Envelopes -- 6.1 ℱ-preenvelopes and Envelopes -- 6.2 Existence of Preenvelopes -- 6.3 Existence of Envelopes -- 6.4 Direct Sums of Envelopes -- 6.5 Flat Envelopes -- 6.6 Existence of Envelopes for Injective Structures -- 6.7 Pure Injective Envelopes -- 7 Covers, Envelopes, and Cotorsion Theories -- 7.1 Definitions and Basic Results -- 7.2 Fibrations, Cofibrations and Wakamatsu Lemmas -- 7.3 Set Theoretic Homological Algebra -- 7.4 Cotorsion Theories with Enough Injectives and Projectives -- 8 Relative Homological Algebra and Balance -- 8.1 Left and Right ℱ-resolutions -- 8.2 Derived Functors and Balance -- 8.3 Applications to Modules -- 8.4 ℱ-dimensions -- 8.5 Minimal Pure Injective Resolutions of Flat Modules -- 8.6 λ and μ-dimensions.

9 Iwanaga-Gorenstein and Cohen-Macaulay Rings and Their Modules -- 9.1 Iwanaga-Gorenstein Rings -- 9.2 The Minimal Injective Resolution of R -- 9.3 More on Flat and Injective Modules -- 9.4 Torsion Products of Injective Modules -- 9.5 Local Cohomology and the Dualizing Module -- 10 Gorenstein Modules -- 10.1 Gorenstein Injective Modules -- 10.2 Gorenstein Projective Modules -- 10.3 Gorenstein Flat Modules -- 10.4 Foxby Classes -- 11 Gorenstein Covers and Envelopes -- 11.1 Gorenstein Injective Precovers and Covers -- 11.2 Gorenstein Injective Preenvelopes -- 11.3 Gorenstein Injective Envelopes -- 11.4 Gorenstein Essential Extensions -- 11.5 Gorenstein Projective Precovers and Covers -- 11.6 Auslander's Last Theorem (Gorenstein Projective Covers) -- 11.7 Gorenstein Flat Covers -- 11.8 Gorenstein Flat and Projective Preenvelopes -- 11.9 Kaplansky Classes -- 12 Balance over Gorenstein and Cohen-Macaulay Rings -- 12.1 Balance of Hom(-, -) -- 12.2 Balance of - ⊗ - -- 12.3 Dimensions over n-Gorenstein Rings -- 12.4 Dimensions over Cohen-Macaulay Rings -- 12.5 Ω-Gorenstein Modules -- Bibliographical Notes -- Bibliography -- Index.