域是有理数集合、实数集合、复数集合的抽象模型，因此在整个数学科学中处于基础地位。Galois是*早提出有限域观点的人，他对于抽象域理论的诞生至关重要。 本书把抽象域论一分为二，首先讲代数扩张及其在代数域论上的应用，其次介绍超越扩张及其在代数函数论及代数几何上的应用，中间还插入经典的Galois理论，使读者对于实际背景有比较清楚的认识。

Preface
Notes to the Reader
List of Symbols
I Galois Theory
1 Field Extensions
2 Automorphisms
3 Normal Extensions
4 Separable and Inseparable Extensions
5 The Fundamental Theorem of Galois Theory
II Some Galois Extensions
6 Finite Fields
7 Cyclotomic Extensions
8 Norms and Traces
9 Cyclic Extensions
10 Hilbert Theorem 90 and Group Cohomology
11 Kummer Extensions
III Applications of Galois Theory
12 Discriminants
13 Polynomials of Degree 3 and 4
14 The Transcendence of and e
15 Ruler and Compass Consturctions
16 Solvability by Radicals
Ⅳ Infinite Algebraic Extensions
Ⅴ Transcendental Extensions
Appendix A Ring Theory
Appendix B Set Theory
Appendix C Group Theory
Appendix D Vector Spaces
Appendix E Topology
References
Index