  We establish the local and global theory for the Cauchy problem of the
singular Hartree equation in three dimensions, that is, the modification of the
non-linear Schr\"odinger equation with Hartree non-linearity, where the linear
part is now given by the Hamiltonian of point interaction. The latter is a
singular, self-adjoint perturbation of the free Laplacian, modelling a contact
interaction at a fixed point. The resulting non-linear equation is the typical
effective equation for the dynamics of condensed Bose gases with fixed
point-like impurities. We control the local solution theory in the perturbed
Sobolev spaces of fractional order between the mass space and the operator
domain. We then control the global solution theory both in the mass and in the
energy space.
