This book includes several lectures given at the DMV Seminar "Classical Nonintegrability, Quantum Chaos." The aim of these lectures was to provide an introduction to the ideas and mathematical techniques of classical and quantum nonlinear dynamics. The lecture by Viviane Baladi gives a much-needed overview of the current literature and includes an informal discussion of the pertinent problems and results. The chapters on irregular scattering and on expanding maps illustrate techniques in nonlinear dynamics using the simplest nontrivial examples. The chapters on quantum chaos an on Liouville surfaces stress a phase space geometry approach to semi-classical quantum theory.