In the last decade, investigations of nonlinear phenomena have developed into a very active research field. The fundamental insight is that the simplest laws of nature can lead to bewilderingly complex dynamics, and that at the same time such dynamics exhibits universal features largely independent of the details of the particular underlying dynamical system. The new vistas, opened in no small part by the advent of modern computation, represent a natural and healthy shift in some research directions. Stressing the unity of the underlying concepts and benefitting from the accumulated experience of scientists of diverse backgrounds, they have transformed important problems that, until recently, have been considered intractable or even ill-posed, into promising new fields. Today a glance at the contents of leading professional publications reveals that nonlinear science has had a significant impact on a broad spectrum of natural sciences. Methods developed in the study of nonlinear systems are routinely applied to such areas as turbulence, quantum theory, nuclear physics, atomic physics, biological control and self-organization, astronomy, cardiology, chemical reactions, nonlinear waves and diffusion, semiconductors, Josephson junctions and problems of classical mechanics (to name some that we have been interested in).