This book has a parent, Ian R. Porteous’ earlier book on Topological Geometry (1969; Zbl 0186.06304). It extends the study on Clifford algebras, spin groups, Cayley algebra and the triality of Spin(8). As a new topic it contains a study of the conformal groups by the Vahlen matrices.
In his review on this book’s parent Jean Dieudonné, the author of Sur les groupes classiques (1948; Zbl 0037.01304) says: “Clifford’s geometric algebra [is] taking pride of place”. In recent years Clifford algebras have indeed become a more popular tool in theoretical physics.
The central theme in the present book is the classification of the reversion and conjugation anti-involutions of the Clifford algebras. This means classification of the automorphism groups of scalar products on spinor spaces; e.g. the automorphism group of Dirac spinors is \(U(2,2)\). The author’s belief is that the “subject only makes sense when the full picture is unfolded”, and that “most of this often very confusing terminology [in conjunction with Dirac, Majorana and Weyl spinors] can with advantage be dropped”. The reviewer cannot but agree with the author’s opinion.
The book is suitable for the last year of an undergraduate course or the first year of a postgraduate course. As its parent, this book can be expected to become a classic.