  The modified newtonian dynamics (MOND) paradigm of Milgrom can boast of a
number of successful predictions regarding galactic dynamics; these are made
without the assumption that dark matter plays a significant role. MOND requires
gravitation to depart from Newtonian theory in the extragalactic regime where
dynamical accelerations are small. So far relativistic gravitation theories
proposed to underpin MOND have either clashed with the post-Newtonian tests of
general relativity, or failed to provide significant gravitational lensing, or
violated hallowed principles by exhibiting superluminal scalar waves or an
\textit{a priori} vector field. We develop a relativistic MOND inspired theory
which resolves these problems. In it gravitation is mediated by metric, a
scalar field and a 4-vector field, all three dynamical. For a simple choice of
its free function, the theory has a Newtonian limit for nonrelativistic
dynamics with significant acceleration, but a MOND limit when accelerations are
small. We calculate the $\beta$ and $\gamma$ PPN coefficients showing them to
agree with solar system measurements. The gravitational light deflection by
nonrelativistic systems is governed by the same potential responsible for
dynamics of particles. To the extent that MOND successfully describes dynamics
of a system, the new theory's predictions for lensing by that system's visible
matter will agree as well with observations as general relativity's predictions
made with a dynamically successful dark halo model. Cosmological models based
on the theory are quite similar to those based on general relativity; they
predict slow evolution of the scalar field. For a range of initial conditions,
this last result makes it easy to rule out superluminal propagation of metric,
scalar and vector waves.
