I appreciate mathematical rigor insofar as it serves as a deterrent to sloppy reasoning, but I think this book represents a case of the author focusing on the mathematics to the point of obscuring its physical significance. Maybe I owe it to my relative ignorance of differenial geometric concepts, but I found this book practically worthless to my understanding of dynamical systems. I tend to agree with David Griffiths when he states that mathematics is a tool to the physicist; this text makes it the sole focus.