This book is the first comprehensive, systematic account of nonlinear dynamics and chaos, one of the fastest-growing disciplines of applicable mathematics. It is highly illustrated and written in a clear, comprehensive style, progressing gently from the most elementary to the most advanced ideas while requiring little previous knowledge of mathematics. Examples of applications to a wide variety of scientific fields introduce concepts of instabilities, bifurcations and catastrophes, and particular attention is given to the vital new ideas of chaos and non-repeatability in deterministic systems.