  For an arbitrary semisimple Frobenius manifold we construct Hodge integrable
hierarchy of Hamiltonian partial differential equations. In the particular case
of quantum cohomology the tau-function of a solution to the hierarchy generates
the intersection numbers of the Gromov--Witten classes and their descendents
along with the characteristic classes of Hodge bundles on the moduli spaces of
stable maps. For the one-dimensional Frobenius manifold the Hodge hierarchy is
a deformation of the Korteweg--de Vries hierarchy depending on an infinite
number of parameters. Conjecturally this hierarchy is a universal object in the
class of scalar Hamiltonian integrable hierarchies possessing tau-functions.
