  In this paper we attempt a self-contained approach to infinite dimensional
Hamiltonian systems appearing from holomorphic curve counting in Gromov-Witten
theory. It consists of two parts. The first one is basically a survey of
Dubrovin's approach to bihamiltonian tau-symmetric systems and their relation
with Frobenius manifolds. We will mainly focus on the dispersionless case, with
just some hints on Dubrovin's reconstruction of the dispersive tail. The second
part deals with the relation of such systems to rational Gromov-Witten and
Symplectic Field Theory. We will use Symplectic Field theory of $S^1\times M$
as a language for the Gromov-Witten theory of a closed symplectic manifold $M$.
Such language is more natural from the integrable systems viewpoint. We will
show how the integrable system arising from Symplectic Field Theory of
$S^1\times M$ coincides with the one associated to the Frobenius structure of
the quantum cohomology of $M$.
