Nope. If keeps one face toward us (more or less). We never see the other side of the moon. But the Sun does - about 1/2 of the time.
From Wiki
Libration Animation of the Moon as it cycles through its phases. The apparent wobbling of the Moon is known as libration.
The Moon is in synchronous rotation, meaning that it keeps the same face turned toward the Earth at all times. This synchronous rotation is only true on average because the Moon's orbit has a definite eccentricity. As a result, the angular velocity of the Moon varies as it moves around the Earth, and is hence not always equal to the Moon's rotational velocity. When the Moon is at its perigee, its rotation is slower than its orbital motion, and this allows us to see up to eight degrees of longitude of its eastern (right) far side. Conversely, when the Moon reaches its apogee, its rotation is faster than its orbital motion and this reveals eight degrees of longitude of its western (left) far side. This is referred to as longitudinal libration.
Because the lunar orbit is also inclined to the Earth's ecliptic plane by 5.1°, the rotation axis of the Moon seems to rotate towards and away from us during one complete orbit. This is referred to as latitudinal libration, which allows one to see almost 7° of latitude beyond the pole on the far side. Finally, because the Moon is only about 60 Earth radii away from the Earth's center of mass, an observer at the equator who observes the Moon throughout the night moves laterally by one Earth diameter. This gives rise to a diurnal libration, which allows one to view an additional one degree's worth of lunar longitude. For the same reason, observers at both geographical poles of the Earth would be able to see one additional degree's worth of libration in latitude.