  A geometric derivation of $W_\infty$ Gravity based on Fedosov's deformation
quantization of symplectic manifolds is presented. To lowest order in Planck's
constant it agrees with Hull's geometric formulation of classical nonchiral
$W_\infty$ Gravity. The fundamental object is a ${\cal W}$-valued connection
one form belonging to the exterior algebra of the Weyl algebra bundle
associated with the symplectic manifold. The ${\cal W} $-valued analogs of the
Self Dual Yang Mills equations, obtained from a zero curvature condition,
naturally lead to the Moyal Plebanski equations, furnishing Moyal deformations
of self dual gravitational backgrounds associated with the complexified
cotangent space of a two dimensional Riemann surface. Deformation quantization
of $W_\infty$ Gravity is retrieved upon the inclusion of all the $\hbar$ terms
appearing in the Moyal bracket. Brief comments on Non Commutative Geometry and
M(atrix)theory are made.
