  The two-dimensional theory of gravity describing a graviton-dilaton system is
considered. The graviton-dilaton coupling can be fixed such that the quantum
theory remains free of the conformal anomaly for any conformal dimension of the
coupled matter system, even if the dilaton does not appear as Lagrange
multiplier. Interaction terms are introduced and the system is analyzed and
solutions are given at the classical level and at the quantum level by using
canonical quantization.
