This text arose from notes on lectures delivered to M.Sc. students at the University of Bristol in the 1980s. The notes were revised and printed for a course of lectures delivered to postgraduates at the University of Tokyo in 1995. The latter course led to collaboration with Professor Tsutomu Kambe in writing in Japanese the book Ryutai Rikigaku – Anteisei To Ranyu (Fluid Dynamics – Stability and Turbulence), published by the University of Tokyo Press in 1998. The present book is an enlargement in English of the first part of the Japanese book. An advanced draft was prepared for a lecture course given to undergraduates and postgraduates at the University of Oxford in 2001. I am grateful to the many students, at Bristol, Tokyo and Oxford, for their stimulating me to clarify both my ideas and their expression, and their encouragement to learn more. I am especially grateful to Professor Kambe for what I learnt from him and put into the text.

The result is a textbook, not a research monograph. To be sure, many points of current research have been incorporated in the text, but there has been no attempt to lead the reader up to the frontier of current research. So the mathematical theory has been described as simply and briefly as was felt possible, and plenty of worked examples and accessible exercises for students have been included. I have cited many publications, perhaps because the habit of doing so is deeply ingrained, certainly not because I ever imagined that many students care about references, let alone follow them up. The overt intention of including the references is to encourage students' instructors to follow up various details and, most importantly, use still and moving pictures to supplement this book in their teaching.