In theoretical and mathematical physics, twistor theory is a theory proposed by Roger Penrose in 1967, as a possible path to a theory of quantum gravity.In twistor theory, the Penrose transform maps Minkowski space into twistor space, taking the geometric objects from a 4-dimensional space with a Hermitian form of signature (2,2) to geometric objects in twistor space, specified by complex coordinates, called twistors. The twistor approach is especially natural for solving the equations of motion of massless fields of arbitrary spin.Penrose's twistor theory is unique to four-dimensional Minkowski space, with its signature (3,1) metric. At the heart of twistor theory lies the isomorphism between the conformal group Spin(4,2) and SU(2,2), which is the group of unitary transformations of determinant 1 over a four-dimensional complex vector space that leave invariant a Hermitian form of signature (2,2), such as that in the classical group.This book is designed to be a state of the art, superb academic reference work and provide an overview of the topic and give the reader a structured knowledge to familiarize yourself with the topic at the most affordable price possible.The accuracy and knowledge is of an international viewpoint as the edited articles represent the inputs of many knowledgeable individuals and some of the most current knowledge on the topic, based on the date of publication.