Pierre Guillot is a lecturer at the Université de Strasbourg and a researcher at the Institut de Recherche Mathématique Avancée (IRMA). He has authored numerous research papers in the areas of algebraic geometry, algebraic topology, quantum algebra, knot theory, combinatorics, the theory of Grothendieck's dessins d'enfants, and Galois cohomology.
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.
