The study of discrete subgroups of semisimple Lie groups is a field with a long history and, at same time, a very active topic of research. It is at the core of several fields, ranging from differential geometry to number theory and since Margulis's breakthrough in the 70's, it is intimately related with dynamical systems.
While the subsequent developments account for rigidity phenomena, our program will be focused on geometric aspects of flexible discrete groups.