Equatorial Mount
Earth's rotation causes stars and other celestial objects to appear as if they move in the night sky. An equatorial mount compensates for this motion by moving parallel to Earth's rotation. Many equatorial mounts have a clock drive that follows the rotation mechanically, saving the observer from constant adjustments to keep an object in the field of view. An equatorial mount is a little heavy and somewhat difficult for a beginner to become accustomed.
Alt-Azimuth Mount
An alt-azimuth mount moves a telescope in two directions, up and down and side to side. Tracking an object requires adjustments in both directions, much like a gun turret. The alt-azimuth mount is considered more user-friendly and intuitive than an equatorial mount. The simpler design of the alt-azimuth mount makes it a choice for amateur astronomers who wish to build their own telescope.
Refractor
The first telescopes were refractors, which use lenses to magnify images. They are sealed at both ends, preventing temperature changes in the tube from distorting images and reducing the chances of misalignment. Without compensation, however, the lenses cause color rainbows around images. Although they are more expensive to buy and to build than reflector telescopes, refractor telescopes can produce good, high-contrast images of the moon and planets.
Reflector
Reflector telescopes use curved mirrors instead of lenses to gather light. They are popular among amateur astronomers because they are less expensive to buy or make than similarly sized refractors. They also are easier to use when looking at objects high in the sky. Small drawbacks include having to make more adjustments to the alignment of the optics because they are exposed to the outside; this also requires frequent cleaning of the optics.