We calculate the homology groups of hypersurfaces in ℂPⁿ⁺¹, n ≥ 3, with fixed number and, maybe, position of singular points and sufficiently high degree. In the case of quadratic singularities, we use the results of the calculations to give a topological description (as specific as possible) of such a hypersurface by means of decomposing it into a connected sum. In this case the topological type of the hypersurface is determined by its dimension, degree, and the number of singular points. Bibliography: 7 titles.