why thats easy =)
1--Achromatic refractors
The Achromatic refracting lens was invented in 1733 by an English barrister named Chester Moore Hall although it was independently invented and patented by John Dollond around 1758. The design overcame the need for very long focal lengths in refracting telescopes by using an objective made of two pieces of glass with different dispersion, "crown" and "flint glass", to limit the effects of chromatic and spherical aberration. Each side of each piece is ground and polished, and then the two pieces are assembled together. Achromatic lenses are corrected to bring two wavelengths (typically red and blue) into focus in the same plane. The era of the Great refractors in the 19th century saw large achromatic lenses culminating with the largest achromatic refractor ever built, the Great Paris Exhibition Telescope of 1900.
2--Apochromatic refractors
Apochromatic refractors have objectives built with special, extra-low dispersion materials. They are designed to bring three wavelengths (typically red, green, and blue) into focus in the same plane. The residual color error (tertiary spectrum) can be up to an order of magnitude less than that of an achromatic lens. Such telescopes contain elements of fluorite or special, extra-low dispersion (ED) glass in the objective and produce a very crisp image that is virtually free of chromatic aberration. Such telescopes are sold in the high-end amateur telescope market. Apochromatic refractors are available with objectives of up to 553 mm in diameter, but most are between 80 and 152 mm.
3--Equatorial Newtonian reflectors
The first reflecting telescope, built in 1668, is attributed to Sir Isaac Newton. The idea was to replace refracting lenses with a reflecting surface placed on a mirror. This allowed for use of material that was not necessarily transparent... different materials could be used (Pyrex is one of the more common materials used today) that were easier to manufacture in early times. The first reflecting telescopes were made with metal mirrors, because they were easier to make than glass. It wasn't until the 1800's that the first silver-on-glass mirror was utilized. Nowadays, silver reflective coatings have mostly been replaced with aluminum coatings... these coatings do not tarnish or oxidize as quickly as silver, but need to be applied in a chamber. A Newtonian reflector's light gathering source (a concave mirror) is set into the "bottom" of the tube, and a small, flat secondary mirror directs the light into the eyepiece, which sits in the focuser on the upper end of the tube. Remember that Newtonian reflectors do not make good spotting scopes, as the "picture" you will see will be upside-down or sitting on it's "shoulder".
4--Dobsonian Newtonian reflectors
"The Telescope Dobsonian is basically two parts; the OTA (optical tube assembly) and the base. The OTA is typically a Newtonian reflector made with a solid tube or a truss tube assembly. The base of the telescope Dobsonian can be made from almost anything handy and any design you can come up with in your head! (click here for information on building a Newtonian telescope)
Keep in mind the whole purpose of the Telescope Dobsonian style was to have a large diameter telescope that was affordable by a lot more people. You might think of John Dobson as the Henry Ford of the telescope! John Dobson literally brought the telescope to the masses by making it affordable and fun. Â His telescope Dobsonian style enabled a totally new style of astronomy to come about...The Sidewalk Astronomer! "
5--Schmidt-Newtonian telescopes
The optical design of the Schmidt-Newton telescope combines elements from both the Schmidt camera and the Newtonian telescope. In this system the parabolic primary mirror common in newtonian reflector is replaced by a spherical mirror, which introduces spherical aberration. This is corrected by the Schmidt corrector plate, like that used in Schmidt-Cassegrain telescopes. From the Newtonian, it inherits the flat secondary mirror.
i think there are at least 4 more.