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