Preface.- ¿Part I Group cohomology and Galois cohomology: generalities.- 1 Cohomology of finite groups.- 2 Cohomology of cyclic groups.- 3 p-groups, the Tate-Nakayama theorem.- 4 Cohomology of profinite groups.- 5 Cohomological dimension.- 6 First notions of Galois cohomology.- Part II Local fields.- 7 Basic facts about local fields.- 8 Brauer group of a local field.- 9 Local class field theory: the reciprocity law.- 10 The Tate local duality theorem.- 11 Local class field theory: Lubin-Tate theory.- Part III Global fields.- 12 Basic facts about global fields.- 13 Cohomology of the idèles.- 14 Reciprocity law.- 15 The abelianized absolute Galois group of a global field.- Part IV Duality theorems.- 16 Class formations.- 17 Poitou-Tate duality.- 18 Some applications.- Appendix.- A Some results from homological algebra.- B A survey of analytic methods.- References.- Index.

David Harari is a professor at the Université Paris-Sud (Orsay). He is a specialist in arithmetic and algebraic geometry, author of 40 research papers in these fields.