  We report 21-yr timing of one of the most precise pulsars: PSR J1713+0747.
Its pulse times of arrival are well modeled by a comprehensive pulsar binary
model including its three-dimensional orbit and a noise model that incorporates
correlated noise such as jitter and red noise. Its timing residuals have
weighted root mean square $\sim 92$ ns. The new dataset allows us to update and
improve previous measurements of the system properties, including the masses of
the neutron star ($1.31\pm0.11$ $M_{\odot}$) and the companion white dwarf
($0.286\pm0.012$ $M_{\odot}$) and the parallax distance $1.15\pm0.03$ kpc. We
measured the intrinsic change in orbital period, $\dot{P}^{\rm Int}_{\rm b}$,
is $-0.20\pm0.17$ ps s$^{-1}$, which is not distinguishable from zero. This
result, combined with the measured $\dot{P}^{\rm Int}_{\rm b}$ of other
pulsars, can place a generic limit on potential changes in the gravitational
constant $G$. We found that $\dot{G}/G$ is consistent with zero
[$(-0.6\pm1.1)\times10^{-12}$ yr$^{-1}$, 95\% confidence] and changes at least
a factor of $31$ (99.7\% confidence) more slowly than the average expansion
rate of the Universe. This is the best $\dot{G}/G$ limit from pulsar binary
systems. The $\dot{P}^{\rm Int}_{\rm b}$ of pulsar binaries can also place
limits on the putative coupling constant for dipole gravitational radiation
$\kappa_D=(-0.9\pm3.3)\times10^{-4}$ (95\% confidence). Finally, the nearly
circular orbit of this pulsar binary allows us to constrain statistically the
strong-field post-Newtonian parameters $\Delta$, which describes the violation
of strong equivalence principle, and $\hat{\alpha}_3$, which describes a
breaking of both Lorentz invariance in gravitation and conservation of
momentum. We found, at 95\% confidence, $\Delta<0.01$ and
$\hat{\alpha}_3<2\times10^{-20}$ based on PSR J1713+0747.
