Topics in Number Theory: A Journey Towards the Herbrand-Ribet Theorem

A course in algebraic number theory, consisting of two topics. The first topic is the algebraic number theory behind the statement of the Herbrand-Ribet theorem: number fields and their integer rings, local fields, global fields, the statement of class field theory. The second topic is one of the following five: The proof of the Herbrand-Ribet theorem, a proof of class field theory, the theory of cyclotomic fields, quadratic forms and higher composition laws (Bhargava 2001), or the basic theory of elliptic curves.