| 1 | Absolute Values and Discrete Valuations (PDF) |
| 2 | Localization and Dedekind Domains (PDF) |
| 3 | Fractional Ideals, Unique Factorization in Dedekind Domains, Approximation (PDF) |
| 4 | Étale Algebras, Norm and Trace, Bilinear Pairings (PDF) |
| 5 | Factoring Primes in Dedekind Extensions (PDF) |
| 6 | Ideal Norm, Module Index, Dedekind-Kummer Theorem (PDF) |
| 7 | Orders in Dedekind Domains, Splitting of Primes in Galois Extensions (PDF) |
| 8 | Frobenius Elements, The Artin Map, Completions (PDF) |
| 9 | Local Fields, Extensions of Complete DVRs (PDF) |
| 10 | Unramified and Totally Ramified Extensions of Complete DVRs (PDF) |
| 11 | Completing Extensions, The Different and Discriminant Ideals (PDF) |
| 12 | Haar Measure, Places, The Product Formula (PDF) |
| 13 | Minkowski's Bound, Finiteness Results (PDF) |
| 14 | Dirichlet's Unit Theorem (PDF) |
| 15 | Riemann Zeta Function and the Prime Number Theorem (PDF) |
| 16 | Fourier and Mellin Transform, Theta and Gamma Functions, The Functional Equation (PDF) |
| 17 | Primes in Arithmetic Progressions, Dirichlet L-series, The Dedekind Zeta Function (PDF) |
| 18 | The Analytic Class Number Formula, Non-vanishing of Dirichlet L-series (PDF) |
| 19 | The Kronecker-Weber Theorem (PDF) |
| 20 | Intro to Class Field Theory, Ray Class Groups and Ray Class Fields (PDF) |
| 21 | Congruence Subgroups, Conductors, Main Theorems of Global Class Field Theory (PDF) |
| 22 | The Ring of Adeles, Strong Approximation (PDF) |
| 23 | The Group of Ideles, Profinite Groups, Infinite Galois Theory (PDF) |
| 24 | Local Class Field Theory (PDF) |
| 25 | Global Class Field Theory and the Chebotarev Density Theorem (PDF) |
