Course on The theory of $p-$local finite groups

This course aims at being an introduction to the theory of $p-$local finite groups. These are algebraic objects modeled on the homotopy theory associated to p-completed classifying spaces of finite groups. They enable to relate the p-local structure of a finite group to related aspects of the homotopy theory of the resulting p-completed classifying space. The concept also allows for the construction of exotic homotopy types, i.e., spaces which behave from a homotopy theoretic point of view like a p-completed classifying space of a finite group, but in fact are not such spaces. The course will cover topics such as classifying spaces, homology decompositions, the Martino-Priddy-Conjecture, Fusion Systems, Linking Systems, Exotic Fusion, and possibly the concept of partial ordered groups which led to the positive answer to the existence and uniqueness question for linking systems associated to saturated fusion systems.