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These notes arose from a series of lectures first presented at the Scuola Interna zionale Superiore di Studi Avanzati and the International Centre for Theoretical Physics in Trieste in July 1980 and then, in an extended form, at the Universities of Sofia (1980-81) and Bielefeld (1981). Their objective has been two-fold. First, to introduce theorists with some background in group representations to the notion of twistors with an emphasis on their conformal properties; a short guide to the literature on the subject is designed to compensate in part for the imcompleteness and the one-sidedness of our review. Secondly, we present a systematic study of po sitive energy conformal orbits in terms of twistor flag manifolds. They are interpre ted as cl assi ca 1 phase spaces of 'conformal parti cl es'; a characteri sti c property of such particles is the dilation invariance of their mass spectrum which, there~ fore, consists either of the point zero or of the infinite interval 222 o < -p ~ PO - P < = The detailed table of contents should give a thorough idea of the material covered in the text. The present notes would have hardly been written without the encouragement and the support of Professor Paolo Budinich, whose enthusiasm concerning conformal semispinors (a synonym of twistors) -viewed in the spirit of El i Cartan -is having a stimulating influence.
