Nakahara is quite a clear book. The logic is very tight and organized and the exercises are nice - they are short and easy, just to check your understanding. It is a good idea to do all of the exercises because there are not many of them. It is one of the more rigorous "math for physicists" books I have read.<br><br>There are indeed some mistakes, but you should be able to find them. One good thing is that Nakahara points out the physical interpretation of things, like homotopy, so you can get a intuitive feel. A great book!<br><br>The only complaint I have is that the references are pretty bad. Nakahara likes to cite Japanese books which I do not have access to and, anyway, are in Japanese. I wish he would cite classic books that everyone uses.