Does the moon orbit the Earth?

The moon orbits Earth about once every 27.322 days. Viewed from Earth, the moon's orbit is nearly a perfect circle tilted approximately 5 degrees to Earth's orbit. Due to tidal forces, the same side of the moon always faces Earth, so it also rotates about once every 27.322 days.

There is a strong technical argument that the moon orbits the sun as well. If the moon was viewed from the surface of the sun, it clearly orbits the sun as part of a double planetary system with Earth. While one might envision its orbit around Earth and the sun to look like a series of loops, the moon's orbit is actualy a very slightly wavy but mostly elliptical orbit around the sun, just like that of Earth.