"Frobenius manifold" is a term which unifies several phenomena from singularity theory, Gromov-Witten invariants (enumerative geometry), and quantum field theory. In each case, certain functions on moduli spaces can be described in terms of covariant constant sections of a bundle with respect to a flat connection, the Dubrovin connection. The flatness condition can be expressed as a nonlinear p.d.e., the WDVV equation. This leads to a close connection with the theory of integrable systems. In the seminar we will study the work of Dubrovin and some of its applications and generalizations, from arious points of view.