  A model of superconductivity in layered high-temperature superconducting
cuprates is proposed, based on the extended saddle point singularities in the
electron spectrum, weak screening of the Coulomb interaction and
phonon-mediated interaction between electrons plus a small short -range
repulsion of Hund's, or spin-fluctuation, origin. This permits to explain the
large values of $Tc$, features of the isotope effect on oxygen and copper, the
existence of two types of the order parameter, the peak in the inelastic
neutron scattering, the positive curvature of the upper critical field, as
function of temperature etc.
