This study enhances the study of module approximation over commutative rings to module approximation over general rings. Free, torsion free, projective, flat approximations and approximations by modules embeddable in a flat module appear in literature. In this study a slightly different concept of I-flat modules is utilized to study approximations. Covers by I-flat modules and modules embeddable in I-flat modules are thus studied in the newer set up. Also, the links between flat and I-flat covers are explored. In modern literature the terminology of approximation is some times replaced by the...