Based on my own experience of teaching from the first edition, and more importantly
based on the comments of the adopters and readers, I have made
some significant changes to the new edition of the book: Part I is substantially
rewritten, Part VIII has been changed to incorporate Clifford algebras,
Part IX now includes the representation of Clifford algebras, and the new
Part X discusses the important topic of fiber bundles.
I felt that a short section on algebra did not do justice to such an important
topic. Therefore, I expanded it into a comprehensive chapter dealing
with the basic properties of algebras and their classification. This required a
rewriting of the chapter on operator algebras, including the introduction of a
section on the representation of algebras in general. The chapter on spectral
decomposition underwent a complete overhaul, as a result of which the topic
is now more cohesive and the proofs more rigorous and illuminating. This
entailed separate treatments of the spectral decomposition theorem for real
and complex vector spaces.