Mathematics does not exist in isolation but is linked inextricably to the physical world. At the 2003 International Congress of Industrial and Applied Mathematics, leading mathematicians from around the globe gathered for a symposium on the "Mathematics of Real World Problems," which focused on furthering the establishment and dissemination of those links. Presented in four parts, Mathematical Models and Methods for Real World Systems comprises chapters by those invited to this symposium. The first part examines mathematics for technology, exploring future challenges of mathematical technology, offering a wide-ranging definition of industrial mathematics, and explaining the mathematics of type-II superconductors. After lucid discussions on theoretical and applied aspects of wavelets, the book presents classical and fractal methods for physical problems, including a fractal approach to porous media textures and using MATLAB® to model chaos in the motion of a satellite. The final section surveys recent trends in variational methods, focusing on areas such as elliptic inverse problems, sweeping processes, and the BBKY hierarchy of quantum kinetic equations. By virtue of its abstraction, mathematics allows the transfer of ideas between fields of applications. Mathematical Models and Methods for Real World Systems clearly demonstrates this and promotes the kind of cross-thinking that nurtures creativity and leads to further innovation.