  We give a unified description of our recent results on the the
inter-relationship between the integrable infinite KP hierarchy, nonlinear
$\hat{W}_{\infty}$ current algebra and conformal noncompact $SL(2,R)/U(1)$
coset model both at the classical and quantum levels. In particular, we present
the construction of a quantum version of the KP hierarchy by deforming the
second KP Hamiltonian structure through quantizing the $SL(2,R)_k/U(1)$ model
and constructing an infinite set of commuting quantum $\hat{W}_{\infty}$
charges (at least at $k$=1).
