Prof. Kiran Kedlaya
This course is a first course in algebraic number theory. Topics to be covered include number fields, class numbers, Dirichlet's units theorem, cyclotomic fields, local fields, valuations, decomposition and inertia groups, ramification, basic analytic methods, and basic class field theory. An additional theme running throughout the course will be the use of computer algebra to investigate number-theoretic questions; this theme will appear primarily in the problem sets.
OCW has published multiple versions of this subject.
Kedlaya, Kiran. 18.786 Topics in Algebraic Number Theory, Spring 2006. (MIT OpenCourseWare: Massachusetts Institute of Technology), http://ocw.mit.edu/courses/mathematics/18-786-topics-in-algebraic-number-theory-spring-2006 (Accessed). License: Creative Commons BY-NC-SA