Preface -- 1 Basic Concepts -- 1.1 Zorn's lemma, ordinal and cardinal numbers -- 1.2 Modules -- 1.3 Categories and functors -- 1.4 Complexes of modules and homology -- 1.5 Direct and inverse limits -- 1.6 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 -- 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.