The course provides a thorough introduction to algebraic number theory.
Introduction to algebraic numbers and number rings. Ideal factorization, finiteness results on class groups and unit groups, explicit computation of these objects. We also intend to discuss algorithmic aspects using the system Sage (http://sagemath.org).
Undergraduate algebra, i.e., the basic properties of groups, rings, and fields, including Galois theory. This material is covered in first and second year algebra courses in the bachelor program of most universities. See http://www.math.leidenuniv.nl/algebra for the course notes used in Leiden and Delft.
The Intensive course Categories & Modules.