This comprehensive text on the fundamentals of modeling flow and sediment transport in rivers treats both the physical principles and numerical methods for various degrees of complexity. It covers 1-D, 2-D (both depth- and width-averaged), and 3-D models, as well as the integration and coupling of these models. The volume includes a broad selection of numerical methods for open-channel flows, such as the SIMPLE(C) algorithms on staggered and non-staggered grids, the projection method, and the stream function and vorticity method. The many worked examples illustrate various conditions, such as reservoir sedimentation, channel erosion due to dam construction, and channel widening and meandering.