Beginning chapters, suited for undergraduates, introduce vectors, complex numbers, and quaternions as background for material on Clifford algebras. Later chapters, also of interest physicists, treat the quantum mechanics of the electron, electromagnetism, and special relativity. Recent research on Clifford algebras is surveyed, and a new classification of spinors is introduced, based on bilinear covariants of physical observables. Scalar products of spinors are classified by involuntary anti-automorphisms of Clifford algebras. Brauer-Wall groups and Witt rings are discussed, and Cauchy's integral formula is generalized to higher dimensions. The author is affiliated with Helsinki Polytechnic Stadia.