1. Quadratic Equations
2. Cubic Equations
3. Quartic Equations
4. The Creation of Polynomials
5. A Modern Approach to Polynomials
6. Alternative Methods for Cubic and Quartic Equations
7. Roots of Unity
8. Symmetric Functions
9. The Fundamental Theorem of Algebra
10. Lagrange
11. Vandermonde
12. Gauss on Cyclotomic Equations
13. Ruffini and Abel on General Equations
14. Galois
15. Epilogue

Galois' Theory of Algebraic Equations gives a detailed account of the development of the theory of algebraic equations, from its origins in ancient times to its completion by Galois in the nineteenth century. The main emphasis is placed on equations of at least the third degree, i.e. on the developments during the period from the sixteenth to the nineteenth century. The appropriate parts of works by Cardano, Lagrange, Vandermonde, Gauss, Abel and Galois are reviewed and placed in their historical perspective, with the aim of conveying to the reader a sense of the way in which the theory of algebraic equations has evolved and has led to such basic mathematical notions as “group” and “field”. A brief discussion on the fundamental theorems of modern Galois theory is included. Complete proofs of the quoted results are provided, but the material has been organized in such a way that the most technical details can be skipped by readers who are interested primarily in a broad survey of the theory. --- summary provided by publisher