  A covariant reformulation of General Relativity is briefly considered from
three points of view: geometrodynamics, Lagrange-Euler field theory, and gauge
field theory. From a geometrodynamics perspective, a definition of the
reference frame as a differential manifold with an affine connection results in
separation of the respective contributions of inertial and gravitational fields
represented by the affine connection and the tensor of nonmetricity within the
Levi-Civita connection of GR. Resulting decomposition of the Einstein curvature
tensor into affine and nonmetric parts allows to recast Einstein's field
equations in a form invariant with respect to the choice of a reference frame
wherein the gravity is described by nonmetricity of space-time . A covariant
Lagrangian is proposed leading to the same field equation. All three approaches
ultimately lead to the same fully covariant theory of gravitation with a
covariant tensor of energy-momentum of the gravitational field and differential
and integral conservation laws. The role of the frames of reference, as
distinguished from coordinate systems, is discussed.
