  We present the theory of the Dirichlet problem for nonlocal operators which
are the generators of general pure-jump symmetric L\'evy processes whose L\'evy
measures need not be absolutely continuous. We establish basic facts about the
Sobolev spaces for such operators, in particular we prove the existence and
uniqueness of weak solutions. We present strong and weak variants of maximum
principle, and L^\infty bounds for solutions. We also discuss the related
extension problem in C^{1,1} domains.
