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 similar to 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-circle dot) and the companion white dwarf (0.286 +/- 0.012 M-circle dot) as well as their parallax distance 1.15 +/- 0.03 kpc. We measured the intrinsic change in orbital period, (P) over dot(b)(Int), is -0.20 +/- 0.17 ps s(-1), which is not distinguishable from zero. This result, combined with the measured (P) over dot(b)(Int) of other pulsars, can place a generic limit on potential changes in the gravitational constant G. We found that (G) over dot/G is consistent with zero [(-0.6 +/- 1.1) x 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 (G) over dot/G limit from pulsar binary systems. The (P) over dot(b)(Int) of pulsar binaries can also place limits on the putative coupling constant for dipole gravitational radiation kappa(D) = (-0.9 +/- 3.3) 10(-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 (alpha) over cap (3), which describes a breaking of both Lorentz invariance in gravitation and conservation of momentum. We found, at 95% confidence, Delta <0.01 and (3) <2 x 10(-20) based on PSR J1713+0747.