The general forms of field equations and free particle's equations of motion for theories of gravitation are derived from the generalized Lagrangian densities of matter fields and free gravitational fields with the aid of invariant property in the (εmn,ξμ) transformations. The General Relativity, the ECSK theory and the general type R+R2+T2 theory of gravity with torsion are shown all to be the special case of the theory given in this paper.