  We present relativistic analyses of 9257 measurements of times-of-arrival
from the first binary pulsar, PSR B1913+16, acquired over the last thirty-five
years. The determination of the 'Keplerian' orbital elements plus two
relativistic terms completely characterizes the binary system, aside from an
unknown rotation about the line of sight; leading to a determination of the
masses of the pulsar and its companion: 1.438 $\pm$ 0.001 solar masses and
1.390 $\pm$ 0.001 solar masses, respectively. In addition, the complete system
characterization allows the creation of tests of relativistic gravitation by
comparing measured and predicted sizes of various relativistic phenomena. We
find that the ratio of observed orbital period decrease due to gravitational
wave damping (corrected by a kinematic term) to the general relativistic
prediction, is 0.9983 pm 0.0016; thereby confirming the existence and strength
of gravitational radiation as predicted by general relativity. For the first
time in this system, we have also successfully measured the two parameters
characterizing the Shapiro gravitational propagation delay, and find that their
values are consistent with general relativistic predictions. We have also
measured for the first time in any system the relativistic shape correction to
the elliptical orbit, $\delta_{\theta}$,although its intrinsic value is
obscured by currently unquantified pulsar emission beam aberration. We have
also marginally measured the time derivative of the projected semimajor axis,
which, when improved in combination with beam aberration modelling from
geodetic precession observations, should ultimately constrain the pulsar's
moment of inertia.
