A Wolter telescope is a telescope for X-rays using only grazing incidence optics. Visible light telescopes are built with lenses or parabolic mirrors. Neither works well for X-rays. Lenses for visible light are made of a transparent material with an index of refraction substantially different from 1, but there is no equivalent material for x-rays. Conventional mirror telescopes work poorly in the X-rays as well, since the light hits the mirrors at near-normal incidence, where the X-rays are transmitted or absorbed, not reflected.
X-rays mirrors can be built, but only if the angle of incidence is very low (typically 10 arc-minutes to 2 degrees)[1]. These are called glancing incidence mirrors. In 1952, Hans Wolter outlined 3 ways a telescope could be built using only this kind of mirror.[2][3]. Not surprisingly, these are called Wolter telescopes of type I, II, and III. Each has different advantages and disadvantages.[4]