Constructive Methods in Algebraic Number Theory

Number fields are finite extensions of the field of rational numbers. For those fields, Zassenhaus defined four fundamental problems to be solved algorithmically, namely the computation of the maximal order (integral closure of Z), the unit group and the class group (parametrising the multiplicative structure of the field) and finally the Galois group or automorphism group of the normal closure.

This series of lectures aims to show algorithmic solutions to all four problems, indicating open problems, alternative solutions and generalisations.