## ABSTRACT

The purpose of this chapter is to develop a method for embedding a number field K in a real vector space of dimension equal to the degree of K, in such a way that ideals in K map to lattices in this vector space. This clever idea opens the way to applications of Minkowski’s theorem. The embedding is defined in terms of the monomorphismsK → C, and we have to distinguish between those that map K into R and those that do not.