Richard Borcherds: Galois Theory

This is a 25-lecture course, with each lecture being about 30 minutes or so, given online by Richard Borcherds. It gives an introduction to Galois theory.

1. Introduction
2. Field Extensions
3. Splitting Fields
4. Algebraic Closure
5. Finite Fields
6. Normal Extensions
7. Separable Extensions
8. Galois Extensions
9. Examples of Galois Extensions
10. Main Theorem
11. Heptadecagon
12. Fundamental Theorem of Algebra
13. Primitive Elements
14. Abel’s Theorem
15. Kummer Extensions
16. Artin-Schreier Extensions
17. Cubics and Quartics
18. Frobenius Automorphism
19. Cyclotomic Polynomials
20. Wedderburn’s Theorem
21. Norm and Trace
22. Discriminants
23. Hilbert’s Theorem 90
24. Infinite Galois Extensions
25. Transcendental Extensions