Many problems in number theory lead naturally to questions about finite field extensions of the field of rational numbers. The goal of this lecture is to study such finite extensions of Q and their rings of integers. Among other topics, we will cover the following:

- number fields, rings of integers, Dedekind domains

- unique factorization, class groups

- units, Minkowski theory

- cyclotomic fields

- valuations, localizations, completions

- local fields

Further information: Moodle course  (password: name of an important mathematician, hint: rehteoN)