This is the clearest book on fluid dynamics that I've seen. It's perfect for physics students who need a quick review of the subject. It does an amazing job of relating the math to the reality. Many of the problems make reference to research as recent as the 1980's. This book isn't the last word on anything (for example the information on instability is only the beginning), but it's an amazing place to start. As for the down sides, the math requirements in my opinion are a little steeper than the back cover implies. It pretty much assumes that you know complex variables and the residue theorem, and although it avoids the more difficult PDEs, it might help to know some things about them. And this isn't really a down side, but a lot of interesting information is tied to the problems, which may bother some readers.