Basics of spin geometry

In this chapter we define spin structures, spinors, the Dirac operator and discuss the properties we need further on. Unless explicitly mentioned all objects (manifolds, bundles, sections) will be assumed smooth in the whole survey. For the thorough treatment of spin or spin(c) groups, spin or spin(c) structures on vector bundles, representation theory of Clifford algebras and Dirac operators on arbitrary semi-Riemannian Clifford modules we refer to [63, 88, 173].