This volume is a Festschrift for Stephen Smale's 60th birthday; most of the chapters are based on papers given at a symposium in his honor at the University of California at Berkeley. The contributions reflect the breadth of Smale's interests, ranging over a wide variety of fields in pure and applied mathematics. In addition, Smale has provided an autobiographical essay, as well as a record of the lively panel discussions at the symposium. The research contributions include papers on differential topology, mathematical economics, dynamical systems, on the theory of computation, on nonlinear functional analysis, and on various applications in the physical and biological sciences. All are currently active areas of interdisciplinary research.