  We enumerate complex algebraic hypersurfaces in $P^n$, of a given (high)
degree with one singular point of a given singularity type. Our approach is to
compute the (co)homology classes of the corresponding equi-singular strata in
the parameter space of hypersurfaces. We suggest an inductive procedure, based
on intersection theory combined with liftings and degenerations. The procedure
computes the (co)homology class in question, whenever a given singularity type
is properly defined and the stratum possesses good geometric properties. We
consider in details the generalized Newton-non-degenerate singularities. We
give also examples of enumeration in some other cases.
