  The Lorentz covariant theory of propagation of light in the (weak)
gravitational fields of N-body systems consisting of arbitrarily moving
point-like bodies with constant masses is constructed. The theory is based on
the Lienard-Wiechert presentation of the metric tensor. A new approach for
integrating the equations of motion of light particles depending on the
retarded time argument is applied. In an approximation which is linear with
respect to the universal gravitational constant, G, the equations of light
propagation are integrated by quadratures and, moreover, an expression for the
tangent vector to the perturbed trajectory of light ray is found in terms of
instanteneous functions of the retarded time. General expressions for the
relativistic time delay, the angle of light deflection, and gravitational red
shift are derived. They generalize previously known results for the case of
static or uniformly moving bodies. The most important applications of the
theory are given. They include a discussion of the velocity dependent terms in
the gravitational lens equation, the Shapiro time delay in binary pulsars, and
a precise theoretical formulation of the general relativistic algorithm of data
processing of radio and optical astrometric measurements in the non-stationary
gravitational field of the solar system. Finally, proposals for future
theoretical work being important for astrophysical applications are formulated.
