Field and Galois theory

I Galois Theory.- 1 Field Extensions.- 2 Automorphisms.- 3 Normal Extensions.- 4 Separable and Inseparable Extensions.- 5 The Fundamental Theorem of Galois Theory.- II Some Galois Extensions.- 6 Finite Fields.- 7 Cyclotomic Extensions.- 8 Norms and Traces.- 9 Cyclic Extensions.- 10 Hubert Theorem 90 and Group Cohomology.- 11 Kummer Extensions.- III Applications of Galois Theory.- 12 Discriminants.- 13 Polynomials of Degree 3 and 4.- 14 The Transcendence of ? and e.- 15 Ruler and Compass Constructions.- 16 Solvability by Radicals.- IV Infinite Algebraic Extensions.- 17 Infinite Galois Extensions.- 18 Some Infinite Galois Extensions.- V Transcendental Extensions.- 19 Transcendence Bases.- 20 Linear Disjointness.- 21 Algebraic Varieties.- 22 Algebraic Function Fields.- 23 Derivations and Differentials.- Appendix A Ring Theory.- 1 Prime and Maximal Ideals.- 2 Unique Factorization Domains.- 3 Polynomials over a Field.- 4 Factorization in Polynomial Rings.- 5 Irreducibility Tests.- Appendix B Set Theory.- 1 Zorn's Lemma.- 2 Cardinality and Cardinal Arithmetic.- Appendix C Group Theory.- 1 Fundamentals of Finite Groups.- 2 The Sylow Theorems.- 3 Solvable Groups.- 4 Profinite Groups.- Appendix D Vector Spaces.- 1 Bases and Dimension.- 2 Linear Transformations.- 3 Systems of Linear Equations and Determinants.- 4 Tensor Products.- Appendix E Topology.- 1 Topological Spaces.- 2 Topological Properties.- References.