A Gentle Course in Local Class Field Theory

Part I. Preliminaries:
1. Kummer theory
2. Local number fields
3. Tools from topology
4. The multiplicative structure of local number fields
Part II. Brauer Groups:
5. Skewfields, algebras, and modules
6. Central simple algebras
7. Combinatorial constructions
8. The Brauer group of a local number field
Part III. Galois Cohomology:
9. Ext and Tor
10. Group cohomology
11. Hilbert 90
12. Finer structure
Part IV. Class Field Theory:
13. Local class field theory
14. An introduction to number fields.