The Moon as Seen from Different Latitudes

Why does the Moon's altitude and azimuth (its position along the horizon) vary from night to night? What do people at the equator or in polar regions see?
The Moon is a creature of the tropics: from mid-to-high latitudes, about midnight we look towards the equator to see it at its highest altitude, and it will appear progressively lower as you move away from the tropics. From high latitudes it undulates just above the horizon for multiple days and nights. From whatever latitude, each night the Moon's path and altitude vary because its orbit is tilted relative to the Earth's equator, and due to the fixed axial tilt of the Earth in its orbit, the Moon appears higher in winter than in summer.