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PrefaceChapter 1 Fundamental Concepts1.1 Relations and Lattices1.2 Categories and Functors1.3 Basic Concepts in Semigroups1.4 S-acts and S-homomorphisms1.5 Prime and Semiprime S-acts over Monoids with Zero Chapter 2 Injective and Weakly Injective S-Acts and Related Concepts2.1 Injective S-acts2.2 Weakly Injective S-acts2.3 Completely Right Injective Monoids2.4 Quasi-injective S-acts and Completely Quasi-injective Monoids Chapter 3 Relatively Injective S-acts and Related Concepts3.1 P-injective and Divisible S-acts3.2 Characterization of Monoids by P-injective S-acts3.3 Weakly Regular Monoids and Normal S-acts3.4 Hereditary and Semihereditary Monoids3.5 Hereditary and Cohereditary S-acts3.6 Completely Right FSF-injective MonoidsChapter 4 Projective S-Acts4.1 Projective S-acts4.2 Completely Right Projective Monoids4.3 Quasi-projective S-acts4.4 (x，y)-projective S-acts4.5 Products of Projective S-acts4.6 Projective Acts over Factorisable SemigroupsChapter 5 Flat S-Acts5.1 The Functor 5.2 Flatness and Condition (P)5 3 Strongly Flat S-actsChapter 6 Homological Classification of Monoids by Flatness6.1 Strong Flatness of Condition (P) Acts6.2 Condition (P) Property of Flat Acts6.3 Strong Flatness of Flat Acts6.4 Right Perfect MonoidsChapter 7 Some Topics Relative to Flatness7.1 von Neumann Regular Monoids7.2 Regularity and Flatness of Acts7.3 Relative Flatness and Strongly Faithful Acts7.4 Purity of Acts7.5 Flatness in SPOSChapter 8 Sheaves for Classes of Monoids8.1 A Historical Introduction of Sheaf Theory in Algebra8.2 Sheaves of von Neumann Regular Monoids with Zero8.3 Pure Ideals of a Monoid with Zero8.4 Pure Spectrum of a Monoid with Zero8.5 S-acts8.6 First Representation Theorem8.7 Second Representation TheoremBibliographyIndex