An introduction to modern research directions and scholarship in nonlinear dynamics, and a reference for researchers in the field. The scholarly level is aimed at the beginning postgraduate student, with a potential readership drawn from disciplines in mathematics and the physical sciences. In addition to pedagogical material, each chapter provides a review of the current state of the area and a discussion on open problems. The contributors include Brian Davies (bifurcations in maps), Nalini Joshi (integrable systems and asymptotics), Alan Newell (wave turbulence and pattern formation), Carl Weiss (spatial solitons), Cathy Holmes (Hamiltonian systems), Tony Roberts (dissipative fluid mechanics), John Brindley (nonlinear dynamics in the oceans) and Mike Lieberman (Fermi acceleration).