ABSTRACT
Most of the material in this chapter is intended for mathematicians, physicists, and practitioners, who wish to refresh their knowledge in scattered areas of mathematics that constitute the fundamentals of the theory of cosmic backgrounds. In a unified style, we introduce elements of linear algebra and representations of compact groups and Clifford algebras over real numbers, complex numbers, and quaternions. The most important representations of Clifford algebras (resp., compact groups) act in linear spaces of spinors (resp., in Hilbert spaces of square-integrable cross-sections of certain homogeneous fibre bundles). Understanding the latter representations require a solid background in differential geometry, which is included. Finally, the chapter also includes the necessary material from variational calculus and probability.
