Brief description:  This course will cover the basic theory of Algebraic Number Fields and Function Fields, their rings of integers and the basic theorems of unique factorization into prime ideals, finiteness of class number and Dirichlet's unit theorem. We will take the approach of Artin and Whaples and give an axiomatic characterization of Number Fields and Function Fields. Here is their original paper.
 

Prerequisite:  Graduate Algebra
 

Textbook:  None. But here is a long list of lecture notes on number theory, some of which are relevant.    
 

Course notes:  Each student will be required to take notes for a week and TeX them.

Here is the whole course available as one file.