The lectures begin by reviewing K-theory and the Bott periodicity theorem. Much of the Baum-Connes theory has to do with broadening the periodicity theorem in one way or another, and for this reason quite some time is spent formulating and proving the theorem in a way which is suited to later extensions. Following that, the lectures turn to the machinery of bivariant -theory and the formulation of the Baum-Connes conjecture. The main objective of the notes is reached in Lecture 4, where the conjecture is proved for groups which act properly and isometrically on affine Euclidean spaces. The remaining lectures deal with partial results which are important in applications and with counterxamples to various overly optimistic strengthenings of the conjecture.