  This note is addressed to giving a short introduction to control theory of
stochastic systems, governed by stochastic differential equations in both
finite and infinite dimensions. We will mainly explain the new phenomenon and
difficulties in the study of controllability and optimal control problems for
these sort of equations. In particular, we will show by some examples that both
the formulation of stochastic control problems and the tools to solve them may
differ considerably from their deterministic counterpart.
