Einführung in die Homotopietheorie

The goal of this course is an introduction to homotopy theory. The main goal is to understand the set of homotopy classes of maps between two spaces. We will develop tools for calculations of homotopy groups like fibre and cofibre sequences and simplicfications like stabilization. We will observe that infinite loop spaces as targets are particularly amenable and provide generalized homology theories. We will meet various examples. A good outcome of the course could be a calculation of the homology of classifying spaces like BU and an understanding of its geometric consequences.