Although many credit Isaac Newton with the invention if the first reflecting telescope, after some research I have found that the concept of a reflecting telescope came from a Scottish mathematician James Gregory. He published a description of the reflecting telescope in "Optica Promota" in 1663, however he never actually made the telescope. Sir Isaac Newton did construct the first reflecting telescope in 1668. I guess it depends on how you define invention. Reflecting telescopes are often called Newtonians.
Reflecting Telescopes use a mirror to gather light and bring the image to the eyepiece. Reflectors utilize a parabolic mirror that reflects the image to a focal point. Since the mirror reflects the image back towards the source, a small secondary mirror set at an angle reflects the light perpendicular to the tube so that the eyepiece is attached to the side of the telescope, rather than the end. Reflectors require some minor maintenance to keep the mirrors in proper alignment. They are the least expensive telescopes and provide the most light-gathering abilities for the dollar.