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Video by NASA Goddard.

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Lunar Libration

At any time, only half of the Moon's surface is visible from Earth, but librations allow us to "peek around the edges." Over time, up to 59% can be observed, although near the edge, where the line of view is very slanted, not much detail can be made out.
Nowadays artificial lunar satellites have mapped the Moon in great detail, so such extra coverage is no big deal.
But before the space age, when astronomers were denied any view of the back of the Moon, any trick for increasing their coverage was appreciated.

Libration 1
The rotation axis of the Earth is inclined by (90°–23.5°) to the Earth-Sun direction which is what gives us our seasons .
Similarly the Moon is inclined by about (90°–6.5°) to the mean Moon-Earth line. That line is also the direction of the Moon’s elongation, on the average always pointed towards Earth.
The 23.5° tilt of the Earth axis lets the Sun shine onto the polar caps, onto circular areas around the poles, giving them 24-hour sunlight. 
Each lunar orbit, the tilt of the Moon’s rotation axis allows observers on Earth to peek into the polar regions of the Moon - at some time into the northern one, half a month later into the southern one. 
Because the tilt is much smaller (only 6.5°), the area thus revealed is much smaller, but still, this increases coverage.
This polar shift can be seen as one effect in the animation.

Libration 2
Suppose the moon moved with steady speed in a perfectly circular orbit around Earth, and also rotated at a steady rate around its axis. 
The Moon’s orbital motion starts from the bottom and advances counter-clockwise, and the Moon itself also rotates counter-clockwise. Then - neglecting the 6.5° tilt - the axis of the Moon could always point straight at the Earth, always exposing the same range of longitudes on the Moon’s surface. By the time the Moon has orbited 360° the Moon itself has also rotated (spun) a full 360°.
However, the orbiting motion of the Moon is not steady – at some times it advances faster than average, some times it is slower. 
The actual orbit of the Moon around Earth is not a circle but an ellipse, an oval shape (not greatly different from a circle). Its distance from Earth, therefore, goes up and down slightly. The Moon speeds up when closer to Earth, and slows down when further away.

Libration 3
A third “libration” arises because the size of the Earth is not negligible. During the 12 hours or so when the Moon is visible on any day, the rotation of the Earth can displace an observer by up to one diameter of the Earth (for observers on the equator), shifting the line of view and slightly increasing the observable area. 
Similarly, observers in the northern and the southern hemisphere get slightly different views. Since this effect again allows astronomers to “peek past the edge,” it too is counted as a sort of libration. 
At a lunar distance of 60 RE (Earth radii), a displacement of 1 RE shifts the viewing angle by about 1°.