Nonlinear science emerged in its present form following a series of decisive analytic, numerical and experimental developments that took place in close interaction in the last three decades. Its aim is to provide the concepts and the techniques necessary for a unified description of the particular, yet quite large, class of phenomena whereby simple deterministic systems give rise to complex behavior associated with the appearance of unexpected spatial structures or evolutionary events. Such systems are encountered in a great number of disciplines notably in classical mechanics, statistical physics, fluid dynamics, chemistry, optics, atomic and molecular physics, environmental sciences, engineering sciences or biology, in the context of both fundamental and applied investigations.

While the concern for unification is central in every attempt of man to explain the natural world, the particular approach followed by nonlinear science in the pursuit of this goal is characterized by a great originality that differentiates it from other disciplines belonging to the traditional realm of physical sciences. Nonlinear science introduces a new way of thinking based on a subtle interplay between qualitative and quantitative techniques, between topological, geometric and metric considerations, between deterministic and statistical aspects. It uses an extremely large variety of methods from very diverse disciplines, but through the process of continual switching between different views of the same reality these methods are cross-fertilized and blended into a unique combination that gives them a marked added value.