Geomorphology deals with some of the most striking patterns of nature. From mountain ranges and mid-ocean ridges, to river networks and sand dunes, there is a whole family of forms, structures, and shapes that demand rationalization as well as mathematical description. In the various chapters of this volume, many of these patterns will be explored and discussed, and attempts will be made to both unravel the reasons for their very existence and to describe their dynamics in quantitative terms. Particular focus will be on lava and mud flows, ice and snow dynamics, river and coastal morphodynamics and landscape formation. Combining a pedagogical approach with up-to-date reviews of forefront research, this volume will serve both postgraduate students and lecturers in search of advanced textbook material, and experienced researchers wishing to get acquainted with the various physical and mathematical approaches in a range of closely related research fields.