  We analyze the symplectic structure of two-dimensional dilaton gravity by
evaluating the symplectic form on the space of classical solutions. The case
when the spatial manifold is compact is studied in detail. When the matter is
absent we find that the reduced phase space is a two-dimensional cotangent
bundle and determine the Hilbert space of the quantum theory. In the
non-compact case the symplectic form is not well defined due to an unresolved
ambiguity in the choice of the boundary terms.
