In these notes we address the canonical quantization of the cosmological
models which appear as solutions of the low energy effective action of closed
bosonic string theory (dilaton models). The analysis is restricted to the
quantization of the minisuperspace models given by homogeneous and isotropic
cosmological solutions. We study the different conceptual and technical
problems arising in the Hamiltonian formulation of these models as a
consequence of the presence of the so called Hamiltonian constraint. In
particular we address the problem of time in quantum cosmology, the
characterization of the symmetry under clock reversls arising from the
existence of a Hamiltonian constraint, and the problem of inposing boundary
conditions on the space of solutions of the Wheeler-DeWitt equation.