On Quaternions and Octonions

An investigation of the geometry of quaternion and octonion algebras, this work is intended for mathematicians, physicists and crystallographers at any level - from undergraduate to professional - who are interested in symmetries of low-dimensional space. The text can also be used as a text for graduate courses in many mathematical fields, including geometry, group theory, algebra and number theory. Topics covered include: the geometry of complex numbers; quaternions and 3-dimensional groups; quaternions and 4-dimensional groups; the Hurwitz integral quaternions; Moufang loops; octonions and 8-dimensional geometry; integral octonions; and the octonion projective plane.