We study the self-adjoint operators with so-called singular perturbations.
This kind of perturbations are defined as the operators living in the spaces
constructed by measures supported by null sets. We give a meaning of a
self-adjoint operator to formal sum H+V, where H denotes a Hamiltonian of a
free system and V means a singular perturbation which, in particular, describes
a Hamiltonian of a system located on a null set. We insist on generalized-sum
method for weakly as well as for strongly singular perturbations.