Quadratic forms and quadrics of space over local rings

Relatively recent and new results on the enumeration of classes of projective congruent quadrics and classes of projective equivalent quadrics of projective spaces over a local ring $R=2R$ with nilpotent principal maximal ideal are reflected in the paper. For the case of the basic ring $R$ with nonprincipal maximal ideal, the enumerations of quadrics of projective plane are given up to projective equivalence.