A Gregorian telescope was the first telescope to be designed that uses mirrors instead of lenses. It was invented by the English astronomer John Gregory. Even though it was designed in 1663, it wasn't the first reflecting telescope to be built. Newton's telescope, a different design, was built in 1668. The Gregorian telescope was first built in 1673 by Robert Hooke.
The telescope uses two curved mirrors. The large primary gathers light, and the small secondary reflects the light out the back of the primary mirror. Both mirrors are concave (bowl-shaped).
It is very similar to the Cassegrain telescope, which uses a large concave primary mirror and a small convex secondary mirror.