During the past two decades Roger Penrose's twistor theory has been a continuing source of mathematical inspiration. It is an ambitious theory which aims to reformulate the foundations of physics using conformal and complex geometry. At the heart of twistor theory lies a geometrical transform now known as the Penrose transform.;This book is an exposition of this transform in a fairly general setting. This setting is provided by complex homogeneous spaces and mathematical input is taken from the representation theory of Lie groups.;The book consists mostly of original research not available elsewhere and is intended for physicists and mathematicians with interests in geometry and symmetry. Whilst the material is presented in full generality, there are many examples throughout and special attention is directed towards the twistor theory of Minkowski space.
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