A comprehensive semi-analytic model of the Moon's rotation has been developed and libration tables have been compiled which are suitable for the analysis of lunar laser ranging measurements (Eckhardt, 1981). In the model, the Moon is considered to be rigid, elastic (using a potential disturbance Love number) or anelastic (using a complex Love number), and its gravity potential is represented through its fourth degree harmonics. The Moon is assumed to move about the Earth according to the Analytic Lunar Ephemeris (ALE) of Deprit, Henrard and Rom (Henrard, 1976), and it is torqued by the Earth and Sun. The ALE is supplemented by the additive and planetary perturbations of the improved Lunar Ephemeris (ILE; Eckert et al., 1954) modified for the Earth figure perturbations according to Van Flandern (1976), and with some corrections to resolve minor inconsistencies. The direct effects of the Earth figure and the rotation of the ecliptic are also included in the model. To derive the main libration theory from the ALE, the Euler dynamical equations are solved iteratively using a digital computer to perform all the semi-analytic mathematical manipulations required. The libration perturbations are solved by the computer in two iterations, taking into account cross terms between the main theory and the perturbations. The overall libration model is estimated to be accurate to 0'.'010; this is the truncation level of the tabulated libration series.