本书是一本抽象代数的入门书籍，系统地介绍了抽象代数中的集合论、群论、环论和域论的相关知识。本书第一章讲述了集合的运算以及分类的基本思想方法，给出了中国剩余定理。第二章讲述了群的定义与一些常见的群，如循环群、置换群、二面体群等。第三章讲述了群的一些基本理论和构造，如正规子群、商群，群的同态和同构。第四章讲述了环论和域论的基本概念和理论，包括环和域的定义及例子，理想、商环、环同态以及域的扩张理论。本书正文内容为英文，后附教学PPT，方便查阅核心内容。本书内容按照48课时设置，可作为教材，也适合初学者和自学者学习使用。

王艳华，上海财经大学数学学院教授，博士生导师，主要从事非交换代数理论的研究工作。讲授的课程主要包括《抽象代数》《高等代数》《基础代数》《代数理论及其应用》《代数学》《线性代数》《数学模型》等。

Chapter 1 Sets
1.1 Set theory
1.2 Maps
1.3 Equivalence relations and equivalence classes
1.4 Factor sets
1.5 Number theory
1.6 The Chinese Remainder Theorem
拓展阅读·数学家的故事
Chapter 2 Groups
2.1 Definitions and examples
2.2 Subgroups
2.3 Cyclic groups
2.4 Permutation groups
2.5 Dihedral groups
拓展阅读·数学家的故事
Chapter 3 Properties of Groups
3.1 Cosets and Lagrange's Theorem
3.2 Normal subgroups and factor groups
3.3 Homomorphisms of groups
3.4 Isomorphisms of groups
3.5 Fundamental Isomorphism theorem of groups
3.6 Endmorphisms and automorphisms of groups
拓展阅读·数学家的故事
Chapter 4 Rings and Fields
4.1 Rings
4.2 Subrings and Ideals
4.3 Ring homomorphisms
4.4 Maximal ideals and prime ideals
4.5 Extension fields
4.6 Algebraic extensions
拓展阅读·数学家的故事
附录1 Chapter 1教学PPT
1.1 Set theory
1.2 Maps
1.3 Equivalence relations and equivalence classes
1.4 Factor sets
1.5 Number theory
1.6 The Chinese Remainder Theorem
附录2 Chapter 2教学PPT
2.1 Definitions and examples
2.2 Subgroups
2.3 Cyclic groups
2.4 Permutation groups
2.5 Dihedral groups
附录3 Chapter 3教学PPT
3.1 Cosets and Lagrange's Theorem
3.2 Normal subgroups and factor groups
3.3 Homomorphisms of groups
3.4 Isomorphisms of groups
3.5 Fundamental Isomorphism theorem of groups
3.6 Endmorphisms and automorphisms of groups
附录4 Chapter 4教学PPT
4.1 Rings
4.2 Subrings and Ideals
4.3 Ring homomorphisms
4.4 Maximal ideals and prime ideals
4.5 Extension fields
4.6 Algebraic extensions
References