| 1 | Absolute Values and Discrete Valuations (PDF) |
| 2 | Localization and Dedekind Domains (PDF) |
| 3 | Properties of Dedekind Domains (PDF) |
| 4 | Étale Algebras, Norm and Trace (PDF) |
| 5 | Dedekind Extensions (PDF) |
| 6 | Ideal Norms and the Dedekind-Kummer Theorem (PDF) |
| 7 | Galois Extensions, Frobenius, the Artin Map (PDF) |
| 8 | Complete Fields and Valuation Rings (PDF) |
| 9 | Local Fields and Hensel's Lemmas (PDF) |
| 10 | Extensions of Complete DVRs (PDF) |
| 11 | Totally Ramified Extensions and Krasner's Lemma (PDF) |
| 12 | The Different and the Discriminant (PDF) |
| 13 | Haar Measures and the Product Formula (PDF) |
| 14 | The Minkowski Bound and Finiteness Results (PDF) |
| 15 | Dirichlet's Unit Theorem (PDF) |
| 16 | Riemann's Zeta Function and the Prime Number Theorem (PDF) |
| 17 | The Functional Equation (PDF) |
| 18 | Dirichlet L-functions, Primes in Arithmetic Progressions (PDF) |
| 19 | The Analytic Class Number Formula (PDF) |
| 20 | The Kronecker-Weber Theorem (PDF) |
| 21 | Class Field Theory: Ray Class Groups and Ray Class Fields (PDF) |
| 22 | The Main Theorems of Global Class Field Theory (PDF) |
| 23 | The Ring of Adeles, Strong Approximation (PDF) |
| 24 | The Idele Group, Profinite Groups, Infinite Galois Theory (PDF) |
| 25 | Local Class Field Theory (PDF) |
| 26 | Global Class Field Theory, the Chebotarev Density Theorem (PDF) |
