  The Liouville approach is applied to the quantum treatment of the dilaton
gravity in two dimensions. The physical states are obtained from the BRST
cohomology and correlation functions are computed up to three-point functions.
For the $N=0$ case (i.e., without matter), the cosmological term operator is
found to have the discrete momentum that plays a special role in the $c=1$
Liouville gravity. The correlation functions for arbitrary numbers of operators
are found in the $N=0$ case, and are nonvanishing only for specific
``chirality'' configurations.
