Preface
Chapter I.Preliminaries-Groups and Rings
1. Introduction to Groups
2. Quotient Groups and Sylow Subgroups
3. Finite Abelian Groups and Solvable Groups
4. Introduction to Rings
5. Factoring in F[x]
Chapter II. Field Extensions
1. Simple Extensions
2. Algebraic Extensions
3. Splitting Fields and Normal Extensions
Chapter III. The Galois Correspondence
1. The Fundamental Correspondence
2. The Solvable Correspondence
Chapter IV. Applications
1. Constructibility
2. Roots of Unity
3. Wedderburn's Theorem
3. Dirichlet's Theorem and Finite Abelian Groups
Appendix A - Groups
1. Group Actions and the Sylow Theorems
2. Free Groups, Generators and Relations
Appendix B - Factoring in Integral Domains
1. Euclidean Domains and Principal Ideal Domains
2. Prime and Irreducible Elements
3. Unique Factorization Domains
Appendix C - Vector Spaces
1. Subspaces, Linear Independence and Spanning
2. Bases and Dimension
Bibliogr
