This book should be suitable for fourth year university mathematics, physics and engineering students, or for
anyone who has already learned differential geometry but has an uneasy feeling that they may have skimmed over a few too many fine points. The intention here is to replace intuition and hand-waving with a seamless, systematic exposition. However, this is only a definitions book, not a theorems book. The reader must look elsewhere for serious theorems and serious applications. But understanding definitions is obviously an enormously important part of understanding theorems and applications.