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This book is concerned with the response of systems in equilibrium to perturbing forces, and the general theory underlying their behaviour. When a system is in equilibrium it can remain motionless indefinitely, until it is disturbed. Then it may sink back to its original state, or vibrate about the position of rest, or fall over. Also, if the conditions governing the system are slowly changed, the system will adjust itself to the alteration in a smooth fashion, except at critical points, where a tiny change of conditions may lead to a major alteration. Important modern topics to which the author gives serious attention are: elementary catastrophe theory; bifurcation and chaos in the response of driven systems; and phase changes, especially critical points and X-transitions. It is Professor Pippard's belief that all practising physicists and engineers should be aware of the disconcerting possibility of real systems to behave unpredictably and this book is intended to encourage the spread of such an awareness.