本书可以分为三个部分：基础、理论和应用。
第1～4章对拟群理论和拟群的主要类别进行了充分的基本介绍，第5～9章介绍了过去20年来主要在“纯”拟群理论分支中得到的一些结果，第10章和第11章收集了有关拟群在编码理论和密码学中的应用信息。

维克多·谢尔巴科夫，摩尔多瓦人，摩尔多瓦科学院数学与计算机科学研究所首席研究员。他的研究重点是代数（拟群、n元拟群、广群）、编码理论和密码学问题的代数方法。他是140多篇出版物的作者，并且是许多数学期刊的定期审稿人，还是多个期刊的编委会成员，包括《广义李理论及其应用杂志》（Journalof Generalized Lie Theory and Applications)、《拟群与相关系统》(Quasigroup and Related Systems)等。

Foreword
List of Figures
List of Tables
Ⅰ Foundations
1 Elements of quasigroup theory
1.1 Introduction
1.1.1 The role of definitions
1.1.2 Sets
1.1.3 Products and partitions
1.1.4 Maps
1.2 Objects
1.2.1 Groupoids and quasigroups
1.2.2 Parastrophy: Quasigroup as an algebra
1.2.2.1 Parastrophy
1.2.2.2 Middle translations
1.2.2.3 Some groupoids
1.2.2.4 Substitutions in groupoid identities
1.2.2.5 Equational definitions
1.2.3 Some other definitions of e-quasigroups
1.2.4 Quasigroup-based cryptosystem
1.2.5 Identity elements
1.2.5.1 Local identity elements
1.2.5.2 Left and right identity elements
1.2.5.3 Loops
1.2.5.4 Identity elements of quasigroup parastrophes
1.2.5.5 The equivalence of loop definitions
1.2.5.6 Identity elements in some quasigroups
1.2.5.7 Inverse elements in loops
1.2.6 Multiplication groups of quasigroups
1.2.7 Transversals: \"Come back way\"
1.2.8 Generators of inner multiplication groups
1.3 Morphisms
1.3.1 Isotopism
1.3.2 Group action
1.3.3 Isotopism: Another point of view
1.3.4 Autotopisms of binary quasigroups
1.3.5 Automorphisms of quasig.roups
1.3.6 Pseudo-automorphisms and G-loops
1.3.7 Parastrophisms as operators
1.3.8 Isostrophism
1.3.9 Autostrophisms
1.3.9.1 Coincidence of quasigroup paiastrolches
1.3.10 Inverse loops to a fixed loci)
1.3.11 Anti-autotopy
1.3.12 Translations of isotopic quasigroups
1.4 Sub-objects
1.4.1 Subquasigroups: Nuclei and center
1.4.1.1 Sub-objects
1.4.1.2 Nuclei
1.4.1.3 Center
1.4.2 Bol and Moufang nuclei
1.4.3 The coincidence of loop nuclei
1.4.3.1 Nuclei coincidence and identities
1.4.4 Quasigroup nuclei snd center
1.4.4.1 Historical notes
1.4.4.2 Quasigroup nuclei
1.4.4.3 Quasigroup center
1.4.5 Regular permutations
1.4.6 A-nuclei of quasigroups
1.4.7 A-pseudo-automorphisms by isostrophy
1.4.8 Commutators and associatcrs
1.5 Congruences
1.5.1 Congruences of qussigrcups
1.5.1.1 Congruences in universal algebra
1.5.1.2 Normal congruences
1.5.2 Quasigroup homomorphisms
1.5.3 Normal subquasigroups
1.5.4 Normal subloolcs
1.5.5 Antihomomorphisms and endomorphisms
1.5.6 Homotopism
1.5.7 Congruences and isotopism
1.5.8 Congruence permutability
1.6 Constructions
1.6.1 Direct product
1.6.2 Semidirect product
1.6.3 Crossed (quasi-direct) product
1.6.4 n-Ary cressed product
1.6.5 Generalized crosssed product
1.6.6 Generalized singular direet product
1.6.7 Sabinin's product
1.7 Quasigroups and combinatorics
1.7.1 Orthogonality
1.7.1.1 Orthogonality of binary operations
1.7.1.2 Orthogonality of n-ary operations
1.7.1.3 Easy way to construct n-ary orthogonal operations
1.7.2 Partial Latin squares: Latin trades
1.7.3 Critical sets cf Latin squares, Sudoku
1.7.4 Transversals in Latin squares
……
Ⅱ Theory
Ⅲ Applications
A Appendix
A.1 The system of German banknotes
A.2 Outline of the history of quasigroup theory
A.3 On 20 Belousov problems
References
Index
编辑手记