Table of Contents

Orthogonal and Symplectic Geometries.- Tensor Algebras, Exterior Algebras and Symmetric Algebras.- Orthogonal Clifford Algebras.- The Clifford Groups, the Twisted Clifford Groups and Their Fundamental Subgroups.- Spinors and Spin Representations.- Fundamental Lie Algebras and Lie Groups in the Clifford Algebras.- The Matrix Approach to Spinors in Three and Four-Dimensional Spaces.- The Spinors in Maximal Index and Even Dimension.- The Spinors in Maximal Index and Odd Dimension.- The Hermitian Structure on the Space of Complex Spinors—Conjugations and Related Notions.- Spinoriality Groups.- Coverings of the Complete Conformal Group—Twistors.- The Triality Principle, the Interaction Principle and Orthosymplectic Graded Lie Algebras.- The Clifford Algebra and the Clifford Bundle of a Pseudo-Riemannian Manifold. Existence Conditions for Spinor Structures.- Spin Derivations.- The Dirac Equation.- Symplectic Clifford Algebras and Associated Groups.- Symplectic Spinor Bundles—The Maslov Index.- Algebra Deformations on Symplectic Manifolds.- The Primitive Idempotents of the Clifford Algebras and the Amorphic Spinor Fiber Bundles.- Self-Dual Yang-Mills Fields and the Penrose Transform in the Spinor Context.- Symplectic Structures, Complex, Structures, Symplectic Spinors and the Fourier Transform.