  The extended phase space method of Batalin, Fradkin and Vilkovisky is applied
to formulate two dimensional gravity in a general class of gauges. A BRST
formulation of the light-cone gauge is presented to reveal the relationship
between the BRST symmetry and the origin of $SL(2,R)$ current algebra. From the
same principle we derive the conformal gauge action suggested by David, Distler
and Kawai.
