本书是第二版，较第一版有很大的改进。证明更加清晰、详尽。由于多变形对称群和多项式的Galois群的相似性，书中以平面上的多边形对称群为开始。这种相似性可以帮助读者理解书中的有关理论知识。书中也包含了一些新的定理，例如：不可约情形。书中用完整的证明和大量练习清晰、有效地讲述了Galois理论。包括：立方、四次方公式的Galois理论的基本理论；五次Galois大定理的不可解性；立方和四次方Galois群的计算。补充了群论、尺规结构和Galois的早期历史。本书是一本Galois理论简明教程，很适合研究生一年级作为教材学习；也是一本很理想的课外学习书。

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