We have obtained crucial information on the deep lunar interior through a Monte Carlo inversion of a number of fundamental lunar spheroidal free oscillations. The results indicate a homogeneous upper mantle with a velocity and density of 3.75¿1.1 km/s and 3.3¿0.5 g/cm3. A transition between the upper and middle mantle in the range 520--580 km depth also seems to be implied. Middle mantle velocities and densities are 5.4¿1.2 km/s and 3.5¿0.2 g/cm3. Moreover, a velocity decrease is seen in the lower mantle (1150--1450 km depth) consistent with earlier inferences of partial melt in this region. The density seems to increase gradually from 1250 km depth to the center of the moon, where it reaches values indicative of an FeS or silicate composition. ¿ 2001 American Geophysical Union