Abstract
Abstract This chapter introduces and discusses the theory of spinors, as well as some of their prominent applications. Algebraic spinors, classical spinors, and spinor operators are presented and, based upon the periodicity theorem and the Clifford algebras representations, classified for arbitrary fine dimensions and metric signature. The properties of these three different types of spinors are also presented. In addition, pure spinors are introduced, and the triality principle, twistors, and Penrose flagpoles are discussed. The chapter ends with a detailed study of the so-called Weyl spinors, which form the basis of the Penrose and Rindler formalisms.
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