This book investigates the geometry of quaternion and octonion algebras. Following a
comprehensive historical introduction the book illuminates the special properties of 3- and
4-dimensional Euclidean spaces using quaternions leading to enumerations of the corresponding
finite groups of symmetries. The second half of the book discusses the less familiar octonion
algebra concentrating on its remarkable triality symmetry after an appropriate study of
Moufang loops. The authors also describe the arithmetics of the quaternions and octonions. The
book concludes with a new theory of octonion factorization.
