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這本書的第一部分為學習么半群、作用、變形、一致和非交換類別的學生提供了一個相對獨立和寬泛的角度。同時這本書也給出了半群理論，自動機，標準語言和其他半群的應用的背景。么半群圈積，作用和範疇在第二部分有詳細的介紹。該書的第二部分主要集中在么半群的同調分類結果，其中包括Morita類型理論在等值性和二象性和么半群的同調特性。
Mati Kilp, Ulrich Knauer, Alexander V. Mikhalev分別是愛沙尼亞共和國、德國和俄羅斯的知名數學家。本書由他們三人聯合撰寫而成。
Foreword
Introduction
Ⅰ Elementary properties of monoids，acts and categories
1 Sets and relations
2 Groupoids，semigroups and monoids
3 Some classes ofsemigroups
4 Acts over monoids（monoid automata）
5 Decompositions and components
6 Categories
7 Functors
Ⅱ Constructions
1 Products and coproducts
2 Pullbacks and pushouts
3 Free objects and generators
4 Cofree objects and cogenerators
5 Tensorproducts
6 Wreath products of monoids and acts
7 The wreath product of a monoid with a small category
Ⅲ Classes of acts
1 Injectiveacts
2 Divisibleacts
3 Principally weakly injective acts
4 fg—weakly injective acts
5 Weaklyinjective acts
6 Absolutely pure acts
7 Cogenerators and overview
8 Torsion free acts
9 Flatness of acts and related properties
10 Principally weakly flat acts
11 Weaklyfiat acts
12 Flat acts
13 Acts satisfying Condition（P）
14 Acts satisfying Condition（E）
15 Equalizer flat acts
16 Pullback flat acts and overview
17 Projective acts
18 Generators
19 Regular acts and overview
Ⅳ Homological classification of monoids
1 Principal weak injectivity
2 On fg—weak injectivity
3 Weak injectivity
4 Absolute purity
5 Injectivity and overview
6 Torsion freeness and principal weak flatness
7 Weak fiatness
8 Flatness
9 Condition（P）
10 Strong flatness
11 Projectivity
12 Projective generators
13 Freeness and overview
14 Regularity of acts
Ⅴ Equivalence and Duality
1 Adjoint functors
2 Categories equivalent to Act—S
3 Morita equivalence of monoids
4 Endomorphism monoids of generators
5 On Morita duality
Bibliography
Index of symbols
Index
