This book is based on a series of lectures I gave at the 1992 Santa Fe Institute Complex Systems Summer School, and on my Princeton University “Complex Systems, Simple Models” course, offered in academic years 1991–92 through 1993–94. A goal of my teaching, and of this book, is to impart the mathematical tools and, as important, the impulse to build simple models of complex processes falling outside the artificial confines of the established fields. Many fascinating and important problems cry out for rigorous interdisciplinary study. And recent advances in scientific computing have made the construction and “experimental” study of dynamical systems remarkably easy. The stage, in short, is set for new synthetic work, indeed for a new discipline or, perhaps, transdiscipline.