Proper Group Actions and the Baum Connes Conjecture This book contains a concise introduction to the techniques used to prove the Baum Connes conjecture. The Baum Connes conjecture predicts that the K homology of the reduced C^* algebra of a group can be computed as the equivariant K homology of the classifying space for proper actions. The approach is expository but it contains proofs of many basic results on topological K homology and the K theory of C^* algebras. It features a detailed introduction to Bredon homology for infinite groups with applications to K homology. It also contains a detailed discussion of naturality questions concerning the assembly map a topic not well documented in the literature. The book is aimed at advanced graduate students and researchers in the area leading to current research problems