James R. Munkres

This book does an excellent job covering its subject matter in great detail. Munkres does not fudge on a single proof; there are no carelessly thrown about phrases that rely on the reader possessing a strong background in the subject (unlike some other math texts I own), and his explanations are as clear as one could hope. Although some might not like his insistence on using the formality of the theory throughout, I greatly appreciate the rigorous and at the same time insightful exposition.

Among the best mathematical texts I've ever read... really, fun to read.

This is one of those obtuse books where even when you already know everything it is going to say, the presentation is turgid and confusing. The writing is tedious and fails to communicate the interest of topology either from an analytic or a set-theoretic point of view. You could read this whole book three times and still not know why topology was interesting or what it was used for.

Also, the binding is cheap and falls apart easily.

Recommended alternative: General Topology, by Kelley.

I wasn't very happy with this book. It turned out to not be very useful for the class I bought it for because it focuses on Euclidean space, and we were interested in normed vector spaces in general. It's drier than necessary and I thought the proofs were very tedious.