  In this paper we prove the stochastic homeomorphism flow property and the
strong Feller property for stochastic differential equations with sigular time
dependent drifts and Sobolev diffusion coefficients. Moreover, the local well
posedness under local assumptions are also obtained. In particular, we extend
Krylov and R\"ockner's results in \cite{Kr-Ro} to the case of non-constant
diffusion coefficients.
