  The aim of this thesis is to determine possible interactions between the
Standard Model with right-chiral neutrinos and a sector of dark matter composed
of a real scalar, left- and right-chiral fermion and a vector particle, which
are singlets of the Standard Model gauge group. In the introductory chapters we
review the evidence for dark matter and methods of its detection. In the main
part, we present the complete list of gauge singlet operators of dimension not
greater than 4, that consist of the standard sector fields. We obtain also an
analogous list for the dark matter particles. Using both of them, we find the
possible interactions between the two sectors, firstly for the renormalizable
theories, then within the effective theory framework with operators up to
dimension 6, imposing the stability symmetry condition on each dark matter
field. We consider the problem of generation for the effective operators in
underlying, renormalizable gauge theory that includes the Standard Model. It is
shown, which of the operators can be generated in tree-level approximation and
which require a loop.
