  The log-Harnack inequality and Harnack inequality with powers for semigroups
associated to SDEs with non-degenerate diffusion coefficient and non-regular
time-dependent drift coefficient are established, based on the recent papers
\cite{Flandoli, Zhang11}. We consider two cases in this work: (1) the drift
fulfills the LPS-type integrability, and (2) the drift is uniformly H\"older
continuous with respect to the spatial variable. Finally, by using explicit
heat kernel estimates for the stable process with drift, the Harnack inequality
for the stochastic differential equation driven by symmetric stable process is
also proved.
