Papers appearing in this volume are the Invited Talks given at ICIAM 2003, the 5th International Congress of Industrial and Applied Mathematics, held in Sydney over the period July 7 to 11, 2003. The Congress celebrates and describes the contributions of applied mathematics -- as an intellectual creation in its own right, as a foundation stone of technological development, and as an indispensable collaborative partner for other scientific disciplines. These aspects of applied mathematics have held true since the dawn of civilization. They will remain just as important in the new millennium. The authors of these papers are all acknowledged masters of their fields, having been chosen through a rigorous selection process by a distinguished International Program Committee.This volume presents an overview of contemporary applications of mathematics, with the coverage ranging from the rhythms of the nervous system, to optimal transportation, elasto-plasticity, computational drug design, hydrodynamic and meteorological modeling, and valuation in financial markets.