In this paper we provide descriptions of the Whitehead groups with coefficients in a ring for the Hilbert modular group (and its reduced version).We also compute the rational topological K-theory of their reduced C * -algebras.This is done by computing the source of the assembly maps in the Farrell-Jones and the Baum-Connes conjecture respectively.We also construct a model for the classifying space of the Hilbert modular group for the family of virtually cyclic subgroups.