  These are lecture notes for a course on the theory of Clifford algebras, with
special emphasis on their wide range of applications in mathematics and
physics. Clifford algebra is introduced both through a conventional tensor
algebra construction (then called geometric algebra) with geometric
applications in mind, as well as in an algebraically more general form which is
well suited for combinatorics, and for defining and understanding the numerous
products and operations of the algebra. The various applications presented
include vector space and projective geometry, orthogonal maps and spinors,
normed division algebras, as well as simplicial complexes and graph theory.
