  The recent classical nonlocal generalization of Einstein's theory of
gravitation is presented within the framework of general relativity via the
introduction of a preferred frame field. The nonlocal generalization of
Einstein's field equations is derived. The linear approximation of nonlocal
gravity (NLG) is thoroughly examined and the solutions of the corresponding
field equations are discussed. It is shown that nonlocality, with a
characteristic length scale of order 1 kpc, simulates dark matter in the linear
regime while preserving causality. Light deflection in linearized nonlocal
gravity is studied in connection with gravitational lensing; in particular, the
propagation of light in the weak gravitational field of a uniformly moving
source is investigated. The astrophysical implications of the results are
briefly mentioned.
