Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematical physics, the Penrose transform, named after Roger Penrose, is a transformation between massless fields on spacetime and cohomology of sheaves on complex projective space. The projective space in question is the twistor space, a geometrical space naturally associated to the original spacetime, and the twistor transform is also geometrically natural in the sense of integral geometry. The Penrose transform is a major component of classical twistor theory.