There are a few different variations but these are the most common
The following picture shows the light paths and tube assemblies of five of the most common types of telescopes.
There are a variety of different reasons for these types of scopes and they have a wide variety of advantages and disadvantages. I will review a few of the key features.
The Refractor telescope - The oldest type of telescope and the most familiar. These are very popular in beginner scopes. They possess an aperture lens at one end and an eyepiece at the other. The aperture lens is typically made up of a sandwich of lenses.
The Newtonian Reflector - A reflecting telescope uses a mirror rather than a lens and the newtonian uses a smaller flat mirror to direct the light out the side of the tube where the eyepice would be.
Cassegrain - THis type of telescope has a mirror with a hole in the center. This way the light is directed to the back of the telescope. The secondary mirror is not flat as in the newtonian. It is concave. This increases the focal length and gives us better performance. Simple cassegrains like this are not actually made very often. But they are the basis for the next two which are very popular.
Catadioptric Telescopes (Composed of both mirrors and lenses)
Schmidt Cassegrain - The mirror is sphrerical which is more accurate than a parabola. The important thing is that there is a thin curved piece of glass at the front of this telescope. This corrects the spherical mirror.
Maksutov - THis also has a correcting piece of glass in the front and typically the secondary mirror is actually an aluminized circle attached directly to this correcting glass.