Geometric Algebra (Wiley Classics Library)

Rating:
Summary: Interesting, though somewhat eclectic
Review: Anyone who knows me would know that I would rate this book five stars. Artin is an excellent author (see my review of Galois theory), and this book is exceptional even for him. He starts out with a truly riveting description of linear algebra (his way of viewing matrices as homomorphisms of vectors spaces makes a large number of things clear), then group and field theory. These topics require considerable background knowledge, but if you have said knowledge, you won't be disapointed. He then proceeds to go though an interesting discussing of projective geometry. He further describes symplectic and orthogonal geometry, and then goes through the theory of non-commutative determinants. This book is certainly interesting, but I wish that he had also included some algebraic topology (his book on this subject was considerably less readable, and dilluted by another author and a translation to English). Algebraic topology is where algebraic methods in geometry are truly interesting, though his coverage of the somewhat eclectic choice of topics is *really* interesting. I suggest it heartily!