1. A catadioptric telescope is a hybrid of both reflector and refractor telescopes. The name is derived from its components; lenses on refractor telescopes are diotropics, curved mirrors are known as catoptrics.
2. The catadioptric design is advantageous because it offers greater error correction and a wider field of view. Because both lenses and mirrors are employed, the high manufacturing costs of grinding lenses can be mitigated.
3. Just like in reflecting telescopes, mirrors in catadioptric designs can correct spherical and chromatic aberrations created by lenses. Coma, another aberration that is typically a problem with reflecting telescopes, can be corrected with a good catadioptric design.
4. Of all the designs of catadioptric telescopes, the most popular are the Schmidt-Cassegrain and Maksutov-Cassegrain models. Each of these are popular for their comparative ease of use and mobility. Catadioptric telescopes allow all their optical components to be present in a single tube, creating a much more compact and portable telescope.
5. As mentioned, most catadioptric telescopes are of the Schmidt-Cassegrain or Maksutov-Cassegrain variety. Other variations include the Maksutov-Newtonian and Schmidt-Newtonian. The variations all have to do with the thickness of the corrector plate and the angle of reflection.
6. Because they are so popular with amateur astronomers and newcomers, all major optics firms produce a good selection of catadioptric telescopes. You'll find great offerings from Celestron, Bushnell, Galileo, Zhumell, and Meade, among others.