PrefaceChapter I.Preliminaries-Groups and Rings1. Introduction to Groups2. Quotient Groups and Sylow Subgroups3. Finite Abelian Groups and Solvable Groups4. Introduction to Rings5. Factoring in F[x]Chapter II. Field Exteio1. Simple Exteio2. Algebraic Exteio3. Splitting Fields and Normal ExteioChapter III. The Galois Correspondence1. The Fundamental Correspondence2. The Solvable CorrespondenceChapter IV. Applicatio1. Cotructibility2. Roots of Unity3. Wedderburn's Theorem3. Dirichlet's Theorem and Finite Abelian GroupsAppendix A - Groups1. Group Actio and the Sylow Theorems2. Free Groups, Generato and RelatioAppendix B - Factoring in Integral Domai1. Euclidean Domai and Principal Ideal Domai2. Prime and Irreducible Elements3. Unique Factorization DomaiAppendix C - Vector Spaces1. Subspaces, Linear Independence and Spanning2. Bases and DimeionBibliogr