Analysis of 24 years of lunar laser ranging data is used to test the principle of equivalence, geodetic precession, the PPN parameters β and γ, and Ġ/G. Recent data can be fitted with a rms scatter of 3 cm. (a) Using the Nordtvedt effect to test the principle of equivalence, it is found that the Moon and Earth accelerate alike in the Sun's field. The relative accelerations match to within 5×10-13. This limit, combined with an independent determination of γ from planetary time delay, gives β. Including the uncertainty due to compositional differences, the parameter β differs from unity by no more than 0.0014; and, if the weak equivalence principle is satisfied, the difference is no more than 0.0006. (b) Geodetic precession matches its expected 19.2 marc sec/yr rate within 0.7%. This corresponds to a 1% test of γ. (c) Apart from the Nordtvedt effect, β and γ can be tested from their influence on the lunar orbit. It is argued theoretically that the linear combination 0.8β+1.4γ can be tested at the 1% level of accuracy. For solutions using numerically derived partial derivatives, higher sensitivity is found. Both β and γ match the values of general relativity to within 0.005, and the linear combination β+γ matches to within 0.003, but caution is advised due to the lack of theoretical understanding of these sensitivities. (d) No evidence for a changing gravitational constant is found, with \|Ġ/G\|<=8×10-12/yr. There is significant sensitivity to Ġ/G through solar perturbations on the lunar orbit.