I am puzzled why we always see the same side of the Moon even though it is rotating around its own axis apart from revolving around the earth. Shouldn't this only be possible if the Moon is not rotating?
When we say that the Moon rotates, we don't mean relative to an observer on Earth, because we're also rotating. Maybe best is to think of it from the perspective of the Sun. If you were at the centre of the solar system, looking at the Earth, you'd see the Moon rotates once every 28 days or so. That also happens to be the amount of time it takes for the Moon to go all the way around the Earth, and that combination is why, on Earth, we always see the same side. Note that I don't mean an observer on the surface of the Sun, because that's rotating too! I just mean an observer who's situated at the centre of the Sun (and can see through it).
Defining rotation generally depends on to whom its relative. How long does it take for the Earth to show the same face to an observer on Mars? I doubt it's 365 days! But it also isn't useful. What really counts is going around the Sun.
To go a bit further, you might also wonder why the Moon always shows us the same face. It isn't just a co-incidence! It's because of tidal locking. Basically, the Moon is sufficiently big and close to the Earth, so that the Earth pulls on the near side more strongly than the far side. The details are a bit long to reproduce here, but the result is that one side of the Moon always faces us. (Only approximately. The Moon still wobbles a bit, so we end up able to see about 58% of its surface from here: see libration.)
The Moon takes 27 d 7 h 43 min to revolve around the Earth, considering the turning with respect to background stars (sidereal revolution), but 29 d 12 h 44 min when seen from the Sun (synodic) and this is because in this period the Earth has revolved around the Sun (view month).
This latest revolution period is governing Moon phases, eclipses and lunisolar tides. Since the Moon takes the same time to circle in on itself around the Earth, it always presents the same face. This is because the Earth, due to an effect called the gravitational gradient, has slowed the Moon completely.
We always see the same side of the Moon because its rotation period is the same as that of its orbit around the Earth. This is due to a phenomenon which is called Tidal Locking and is actual very frequent for orbiting bodies.
The gravitational interaction between the parent planet and a moon ends up dissipating enough energy that it slows the moon rotation until it presents always the same side. It's a very common occurrence even in the Solar Sytem: Pluto and its moon Charon are tidally locked together (both of them!) and most moons of the Gas Giants (Saturn, Jupiter, Uranus, Neptune) are also tidally locked to their parent planet.
Cf Wikipedia: http://en.wikipedia.org/wiki/Tidal_locking
My hypothesis was apparently wrong, probably due to rotation of Earth.
Apparently the Moon is rotating the same way as Earth does. That would lead to the hypothesis that the Earth and the Moon came up from some mass, not necesarily continous, but all having the same centre of gravity and rotation. Then, the Earth and Moon was formed from this mass, probably due to gravity, but there was already no external power which would change the rotation somehow, so the rotation of all the mass remained after creation of the Earth and the Moon.)
I believe that the answer might be due to one side of the moon being denser (heavier). An example is if you take a ball and add a heavy weight to one spot on the ball, the heavier spot on the ball will always rotate to the bottom towards the strongest gravity. Same situation on the moon if one side is denser, then that side will always face us due to the gravitational pull of the earth. If the moon was rotating faster at one time, it would eventually slow down and face the earth just as a ball would eventually stop rolling around when released and stop with the heavy side facing down towards gravity. One of the latest theories is that the earth was struck by a large body and the moon was generated from that debris. It would have been possible to end up with heavier (more mass) on one side of the moon. There was a report recently that in fact stated that the mineral composition of the back side of the moon was different from the front side of the moon which would fit my proposition. I believe that the same situation may apply to mercury also since the same side always faces the sun. I believe that it is too much of a coincidence that the moon just happens to rotate at the correct speed and the unequal mass distribution provides a very plausible answer.