本書是第二版，較**版有很大的改進。證明*加清晰、詳盡。由於多變形對稱群和多項式的Galois群的相似性，書中以平面上的多邊形對稱群為開始。這種相似性可以幫助讀者理解書中的有關理論知識。書中也包含了一些新的定理，例如：不可約情形。書中用完整的證明和大量練習清晰、有效地講述了Galois理論。包括：立方、四次方公式的Galois理論的基本理論；五次Galois大定理的不可解性；立方和四次方Galois群的計算。補充了群論、尺規結構和Galois的早期歷史。本書是一本Galois理論簡明教程，很適合研究生一年級作為教材學習；也是一本很理想的課外學習書。

Preface to the Second Edition
Preface to the First Edition
To the Reader
Symmetry
Rings
Domains and Fields
Homomorphisms and Ideals
Quotient Rings
Polynomial Rings over Fields
Prime Ideals and Maximal Ideals
Irreducible Polynomials
Classical Formulas
Splitting Fields
The Galois Group
Roots of Unity
Solvability by Radicals
Independence of Characters
Galois Extensions
The Fundamental Theorem of Galois Theory
Applications
Galois's Great Theorem
Discriminants
Galois Groups of Quadratics. Cubics, and Quartics
Epilogue
Appendix A: Group Theory Dictionary
Appendix B: Group Theory Used in the Text
Appendix C: Ruler-Compass Constructions
Appendix D: Old-fashioned Galois Theory
References
Index