This is a really excellent and much-needed book, cross-cutting between, and showing the inter-relations between, the various fields of mathematics which are usually taught (for good reason) in isolation from each other in the academic curriculum.
There is one omission I want to point out:
There is an excellent elementary introduction to category theory, assuming nothing more than high school math:
"Conceptual Mathematics" by F. William Lawvere and Stephen Schanuel.
So, Stillwell is overstating things when he writes in his Section 10.9
"category theory [necessarily?] involves a high level of abstraction, and background too advanced for a book such as this".
