Analysis on Manifolds

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.

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.