- Hilbert's theory of ramification (Galois theory applied to the decomposition of prime ideals)
- The Frobenius automorphism and the Artin symbol
- Zeta functions and L-series
- Frobenius density theorem
- The first inequality
- Herbrand's Lemma and a little bit of cohomology
- The second inequality
- Artin reciprocity

It is almost impossible to cover class field theory in one semester (except by using all the fancy tools mentioned above), so occasionally I might have to sketch a proof or two, in particular since I also would like to briefly sketch a few important topics, such as

- Artin L-functions and representation theory
- Galois representations
- class field towers
- principal ideal theorem
- reciprocity laws

- Th 01.02.: problems 1.3, 1.4, 1,6, 1.10, 1.11
- Tu 13.02.: problems 2.1, 2.4, 2.5, 2.6, 2.7
- Tu 06.03.: problems 1.9 - 1.13 from the new chapter 1.
- Tu 20.03.: problems 3.1 - 3.4
- We 04.04.: problems 6.2, 6.6, 6.7
- Tu 01.05.: problems 11.5 - 11.9

Noah Snyder's historical account of Artin's L-functions can be found here.

Anatoly Preygel has written a paper on L-functions and density of primes.

Here are a few expositions of parts of Janusz's book by Daileda and Goins.

Here's a nice article by Lenstra and Stevenhagen on Chebotarev and his density theorem.

- Tu 30.01. Review of Algebraic Number Theory
- Th 01.02. Review of Algebraic Number Theory
- Tu 06.02. Galois Extensions and Ramification Groups; Artin symbol
- We 07.02. 13:40 - 14:30 Quadratic Reciprocity; Hilbert Class Fields
- Tu 13.02. Hilbert class fields, Generalized class groups
- We 14.02. No class; moved to 28.02
- Tu 20.02. Generalized class groups; analytic methods
- We 21.02. Riemann zeta function; infinitude of primes
- Tu 27.02. Dirichlet's computation of L(1); Dirichlet density
- We 28.02. Quadratic class number formula I; homework
- Tu 06.03. Class number formula for quadratic fields II.
- We 07.03. Dirichlet's Theorem on Primes in Arithmetic Progression
- Tu 13.03. Nonvanishing of L-series at s=1
- We 14.03. Factorization of the zeta function of cyclotomic fields
- Tu 20.03. Minkowski bounds; Dirichlet's unit theorem
- We 21.03. Dedekind's class number formula
- Tu 27.03. Dedekind's class number formula
- We 28.03. Prime ideal decomposition in nonnormal extensions
- Tu 03.04. Frobenius density theorem
- We 04.04. First Inequality
- spring break
- Tu 17.04. Preparations for the second inequality
- Th 18.04. Index calculations
- Tu 24.04. Herbrand quotient of units
- Th 25.04. Herbrand's unit theorem
- Tu 01.05. Main Theorems of Class Field Theory
- Th 02.05. Examples of Hilbert Class Fields
- Tu 08.05. Artin reciprocity and the existence theorem (sketch)
- Th 09.05. Norm residues and Local class field theory; ideles (sketch)