This work translates new mathematical ideas in nonlinear dynamics and chaos into a language that engineers and scientists can understand, and gives specific examples and applications of chaotic dynamics in the physical world. Also describes how to perform both computer and physical experiments in chaotic dynamics. The topics cover Poincare maps, Fractal dimensions, and Lyapunov exponents, illustrating their use in specific physical examples. It includes an extensive guide to the literature, especially that relating to more mathematically oriented works; a glossary of chaotic dynamics terms; a list of computer experiments; and details for a demonstration experiment on chaotic vibrations.