The seminar will be a report on the exciting recent development in von Neumann algebra theory due to Sorin Popa and his collaborators. The seminar will be based on the two papers by Popa, which started it all, and a survey paper by Stefan Vaes about the more recent development: S. Popa, On a class of Type II_1 Factors with Betti number invariants, Annals of Math. 163 (2006), 809-899 S. Popa, On the fundamenntal group of type II_1 factors, Proc. Nat. Acad. Sci. 101 (2004), 723-726.