The Shanghai Forum on Industrial and Applied Mathematics was organized in May 2006 on the occasion that many famous industrial and applied mathematicians gathered in Shanghai from different countries to participate in the Officers'' Meeting and the Board Meeting of the ICIAM (International Council for Industrial and Applied Mathematics). This volume collects the material covered by the majority of the lectures of which reflects panoramically recent results and trends in industrial and applied mathematics. This book will be very useful for graduate students and researchers in industrial and applied mathematics.