This book is about the higher dimensional complex numbers. Although it was not known when the first edition was printed, the higher dimensional complex numbers are spinor spaces and the classical spaces, including our 4-dimensional space-time, arise from these spinor spaces by superimposition of isomorphic algebras. This book covers the mathematical foundations underlying the mathematics of spinors and the space-time of classical physics. To understand this book, the reader needs no more than an elementary understanding of matrices and an elementary understanding of finite group theory. Previous knowledge of complex numbers would be helpful.