  In this paper we establish a general form of the Mass Transference Principle
for systems of linear forms conjectured in [1]. We also present a number of
applications of this result to problems in Diophantine approximation. These
include a general transference of Lebesgue measure Khintchine-Groshev type
theorems to Hausdorff measure statements. The statements we obtain are
applicable in both the homogeneous and inhomogeneous settings as well as
allowing transference under any additional constraints on approximating integer
points. In particular, we establish Hausdorff measure counterparts of some
Khintchine-Groshev type theorems with primitivity constraints recently proved
by Dani, Laurent and Nogueira [8].
