[en] We report 21-year 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 short- and long-timescale correlated noise such as jitter and red noise. Its timing residuals have weighted root mean square ∼92 ns. The new data set allows us to update and improve previous measurements of the system properties, including the masses of the neutron star (1.31 ± 0.11 M_⊙) and the companion white dwarf (0.286 ± 0.012 M_⊙) as well as their parallax distance 1.15 ± 0.03 kpc. We measured the intrinsic change in orbital period, ${\stackrel{\dot{}<!--\; ??\; -->}{P}}_{\mathrm{b}}^{\mathrm{I}\mathrm{n}\mathrm{t}}$, is −0.20 ± 0.17 ps s⁻¹, which is not distinguishable from zero. This result, combined with the measured ${\stackrel{\dot{}<!--\; ??\; -->}{P}}_{\mathrm{b}}^{\mathrm{I}\mathrm{n}\mathrm{t}}$ of other pulsars, can place a generic limit on potential changes in the gravitational constant G. We found that $\stackrel{\dot{}<!--\; ??\; -->}{G}/G$ is consistent with zero [(−0.6 ± 1.1) × 10⁻¹² 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 $\stackrel{\dot{}<!--\; ??\; -->}{G}/G$ limit from pulsar binary systems. The ${\stackrel{\dot{}<!--\; ??\; -->}{P}}_{\mathrm{b}}^{\mathrm{I}\mathrm{n}\mathrm{t}}$ of pulsar binaries can also place limits on the putative coupling constant for dipole gravitational radiation ${\mathrm{\kappa <!--\; ??\; -->}}_{\mathrm{D}}=(-<!--\; ???\; -->0.9\pm <!--\; ??\; -->3.3)\times <!--\; ??\; -->{10}^{-<!--\; ???\; -->4}$ (95% confidence). Finally, the nearly circular orbit of this pulsar binary allows us to constrain statistically the strong-field post-Newtonian parameters Δ, which describes the violation of strong equivalence principle, and ${\stackrel{^<!--\; ^\; -->}{\mathrm{\alpha <!--\; ??\; -->}}}_3$, which describes a breaking of both Lorentz invariance in gravitation and conservation of momentum. We found, at 95% confidence, $\mathrm{\Delta <!--\; ??\; -->}<<!--\; <\; -->0.01$ and ${\stackrel{^<!--\; ^\; -->}{\mathrm{\alpha <!--\; ??\; -->}}}_3<<!--\; <\; -->2\times <!--\; ??\; -->{10}^{-<!--\; ???\; -->20}$ based on PSR J1713+0747.