  A path-integral representation for the kernel of the evolution operator of
general Hamiltonian systems is reviewed. We study the models with bosonic and
fermionic degrees of freedom. A general scheme for introducing boundary
conditions in the path-integral is given. We calculate the path-integral for
the systems with quadratic first class constraints and present an explicit
formula for the heat kernel in this case. These results may be applied to many
quantum systems which can be reduced to the Hamiltonian systems with quadratic
constraints (confined quarks, Calogero type models, string and $p$-brain
theories, etc.).
