Quote by TacTics
This seems a bit tautological, though. In the metric topology, open balls are open.... but we're asked to prove that an open by is open? It's a strange problem, if in fact that is how it is stated.

Munkres doesn't spend enough time on the topology to define a basis so, in this context, it's not quite as tautological as it seems. It really only addresses manifolds as subsets of
R^{n} and only covers "real" manifolds with a sketchy last chapter, "Life outside
R^{n}". On the whole though, It's probably the best introduction to the ideas that I've seen. It's a great book.
Petek gave good advice.