| 1 | Absolute values and discrete valuations | |
| 2 | Localization and Dedekind domains | |
| 3 | Properties of Dedekind domains, ideal class groups, factorization of ideals | Problem set 1 due |
| 4 | Étale algebras, norm and trace | |
| 5
| Dedekind extensions | Problem set 2 due |
| 6 | Ideal norms and the Dedekind-Kummer theorem | |
| 7 | Galois extensions, Frobenius elements, and the Artin map | Problem set 3 due |
| 8 | Complete fields and valuation rings | |
| 9 | Local fields and Hensel's lemmas | Problem set 4 due |
| 10 | Extensions of complete DVRs | |
| 11 | Totally ramified extensions and Krasner's lemma | |
| 12 | The different and the discriminant | Problem set 5 due |
| 13 | Global fields and the product formula | |
| 14 | The geometry of numbers | Problem set 6 due |
| 15 | Dirichlet's unit theorem | |
| 16 | Riemann's zeta function and the prime number theorem | |
| 17 | The functional equation | Problem set 7 due |
| 18 | Dirichlet L-functions and primes in arithmetic progressions | |
| 19 | The analytic class number formula | Problem set 8 due |
| 20 | The Kronecker-Weber theorem | |
| 21 | Class field theory: ray class groups and ray class fields | Problem set 9 due |
| 22 | The main theorems of global class field theory | |
| 23 | Tate cohomology | |
| 24 | Artin reciprocity in the unramified case | |
| 25 | The ring of adeles, strong approximation | Problem set 10 due |
| 26 | The idele group, profinite groups, infinite Galois theory | |
| 27 | Local class field theory | |
| 28 | Global class field theory and the Chebotarev density theorem | Problem set 11 due |
