With an emphasis on both theory and experiment, this text describes the behaviour of homogeneous and density-stratified fluids over and around topography. In examining the similarities between the flow of a river over a barrier or weir and the flow of the atmosphere over a mountain range, this book presents a comprehensive synthesis of this topic in terms suitable for scientists, engineers, teachers and students of fluid dynamics. Using the appropriate mathematics, experiments, and illustrations, the text describes the properties of stratified flows beginning with the simplest situations, such as the flow of a homogeneous layer with a free surface - the prototype system for conventional hydraulics, and proceeding to progressively more complex ones, such as the flow of stratified fluid over two- and three-dimensional topography. The book concludes with a discussion of how applications of the properties and principles of these diverse phenomena may be modelled in practical terms.