  The quantum cosmology of two-dimensional dilaton-gravity models is
investigated. A class of models is mapped onto the constrained
oscillator-ghost-oscillator model. A number of exact and approximate solutions
to the corresponding Wheeler-DeWitt equation are presented. A wider class of
minisuperspace models that can be solved in this fashion is identified.
Supersymmetric extensions to the induced gravity theory and the bosonic string
theory are then considered and closed-form solutions to the associated quantum
constraints are derived. The possibility of applying the third-quantization
procedure to two-dimensional dilaton-gravity is briefly discussed.
