Geometric Algebra (book)

Geometric Algebra is a book written by Emil Artin and published by Interscience Publishers, New York, in 1957. It was republished in 1988 in the Wiley Classics series (ISBN 0-471-60839-4).

In 1962 Algèbre Géométrique, a translation into French by Michel Lazard, was published by Gauthier-Villars, and reprinted in 1996. (ISBN 2-87647-089-6) In 1968 a translation into Italian was published in Milan by Feltrinelli.^[1] In 1969 a translation into Russian was published in Moscow by Nauka^[2]

Long anticipated as the sequel to Moderne Algebra (1930), which Bartel van der Waerden published as his version of notes taken in a course with Artin, Geometric Algebra is a research monograph suitable for graduate students studying mathematics. From the Preface:

Linear algebra, topology, differential and algebraic geometry are the indispensable tools of the mathematician of our time. It is frequently desirable to devise a course of geometric nature which is distinct from these great lines of thought and which can be presented to beginning graduate students or even to advanced undergraduates. The present book has grown out of lecture notes for a course of this nature given at New York University in 1955. This course centered around the foundations of affine geometry, the geometry of quadratic forms and the structure of the general linear group. I felt it necessary to enlarge the content of these notes by including projective and symplectic geometry and also the structure of the symplectic and orthogonal groups.

The book is illustrated with six geometric configurations in chapter 2, which retraces the path from geometric to field axioms previously explored by Karl von Staudt and David Hilbert.