  We discuss the quantum theory of 1+1 dimensional dilaton gravity, which is an
interesting model with analogous features to the spherically symmetric
gravitational systems in 3+1 dimensions. The functional measures over the
metrics and the dilaton field are explicitly evaluated and the diffeomorphism
invariance is completely fixed in conformal gauge by using the technique
developed in the two dimensional quantum gravity. We argue the relations to the
ADM formalism. The physical state conditions reduce to the usual Wheeler-DeWitt
equations when the dilaton $\df^2 ~ (=\e^{-2\phi}) $ is large enough compared
with $\kappa =(N-51/2)/12$, where $N $ is the number of matter fields. This
corresponds to the large mass limit in the black hole geometry. A singularity
appears at $\df^2 =\kappa (>0) $. The final stage of the black hole evaporation
corresponds to the region $\df^2 \sim \kappa $, where the Liouville term
becomes important, which just comes from the measure of the metrics. If $\kappa
< 0 $, the singularity disappears.
