1. The revolution of the Moon around the Earth means that, depending on which day it is we see the area illuminated by sunlight in a different position. This is the reason why the appearance of the Moon changes, these changes are called phases.
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2. 1. New Moon
In this phase the Sun illuminates the hidden side of the Moon, which is the side opposite to the one we see from the Earth. This is the reason we cannot see the Moon in the sky.

3. 2. First quarter
Seen from the Earth, the Moon looks like the letter D because the side illuminated by the Sun is the eastern hemisphere of the Moon. It can be seen from midday till midnight.

4. 3. Full Moon
In this case, the Sun illuminates completely the side of the Moon seen from the Earth, since the Moon is in a position opposite the Sun. It can be seen from dusk till dawn.

5. 4. Last quarter
Now the Moon seen from the Earth looks like the letter C, since the Sun illuminates the western hemisphere of the Moon. It can be seen from midnight till midday.