  The aim of this notes is to give a concise introduction to control theory for
systems governed by stochastic partial differential equations. We shall mainly
focus on controllability and optimal control problems for these systems. For
the first one, we present results for the exact controllability of stochastic
transport equations, null and approximate controllability of stochastic
parabolic equations and lack of exact controllability of stochastic hyperbolic
equations. For the second one, we first introduce the stochastic linear
quadratic optimal control problems and then the Pontryagin type maximum
principle for general optimal control problems. It deserves mentioning that, in
order to solve some difficult problems in this field, one has to develop new
tools, say, the stochastic transposition method introduced in our previous
works.
