The Baum Connes conjecture and the Farrel Jones conjecture are important statements in many geometric problems. A central ingredient in their formulation are K-theory groups of C^*-algebras and L-theory groups of rings with involution. We will give a basic introduction and definition of these groups with many examples. Then we explain how these groups (and the underlying spaces) are related and describe results that lead to comparisons between Baum Connes and Farrel Jones conjectures. This is joint work with Markus Land.
