A Wolter telescope is a telescope for X-rays using only grazing incidence optics. Visible light telescopes are built with either lenses or parabolic mirrors at nearly normal incidence (that is, a nearly perpendicular angle of reflection). Neither works well for X-rays. Lenses for visible light are made of a transparent material with an index of refraction substantially different from one, 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 from the plane of reflection is very low (typically 10 arc-minutes to 2 degrees). These are called glancing (or grazing) incidence mirrors. In 1952, Hans Wolter outlined three ways a telescope could be built using only this kind of mirror. These are called Wolter telescopes of type I, II, and III. Each has different advantages and disadvantages.
Wolter's key discovery was that by using two mirrors it is possible to create a telescope with a usably wide field of view. In contrast, a grazing incidence telescope with just one parabolic mirror could focus X-rays, but only very close to the centre of the field of view as it would suffer from extreme coma.