Many mathematical invariants of manifolds can be formulated in terms of homotopy groups. In practice, they are very hard to calculate and require the skillful use of cohomology theories. For some years there is a new family of cohomology theories which uses the theory of elliptic curves and modular forms. It was initiated by the physicist and mathematician Ed Witten who investigated the behavior of small loops (strings) in manifolds. It is the purpose of elliptic cohomology theories to build a mathematical framework for these ideas and to determine the rich algebraic structure of homotopy groups. The talk gives a brief insight into this new world.