Table of Contents:
  • pt. I. Local fields (basic facts). Discrete valuation rings and Dedekind domains
  • Completion
  • pt. II. Ramification. Discriminant and different
  • Ramification groups
  • The norm
  • Artin representation
  • pt. III. Group cohomology. Basic facts
  • Cohomology of finite groups
  • Theorems of Tate and Nakayama
  • Galois cohomology
  • Class formations
  • pt. IV. Local class field theory. Brauer groups of a local field
  • - Local class field theory
  • Local symbols and existence theorem
  • Ramification.