Instability of flows and their transition to turbulence are widespread phenomena in engineering and the natural environment, and are important in applied mathematics, astrophysics, biology, geophysics, meteorology, oceanography and physics as well as engineering. This is a textbook to introduce these phenomena at a level suitable for a graduate course, by modelling them mathematically, and describing numerical simulations and laboratory experiments. The visualization of instabilities is emphasized, with many figures, and in references to more still and moving pictures. The relation of chaos to transition is discussed at length. Many worked examples and exercises for students illustrate the ideas of the text. Readers are assumed to be fluent in linear algebra, advanced calculus, elementary theory of ordinary differential equations, complex variables and the elements of fluid mechanics. The book is aimed at graduate students but will also be very useful for specialists in other fields.

'There is not much to say about this book - if you want to know about hydrodynamic stability, get it, pen and paper, maybe a computer, and start working through it. There is no better way … Anyone who has worked conscientiously through this book will have no trouble moving on to research in this topic.'

Source: The Mathematical Gazette

'Drazin's book is an excellent first introduction to this subject … and a very useful book has been produced that will be of interest to engineers, physicists and mathematicians starting research in fluid mechanics for many years to come.'

Source: The Journal of Fluid Mechanics

'… introduces prospective students into its subject at a graduate level. Without either undue oversimplification or oversophistication the author manages to present the fundamentals of hydrodynamic stability in a very lucid way.'

Source: Monatshefte für Mathematik

'Without either undue oversimplification or over-sophistication the author manages to present the fundamentals of hydrodynamic stability in a very lucid way. The exercises constitute a part of particular value. With their many comments and further thoughts they amount to much more than just to exercises in the plain meaning of the word.'

Source: Internationale Mathematische Nachrichten