With an emphasis on both theory and experiment, this text describes the behavior of homogeneous and density-stratified fluids over and around topography. The topics include the flow of a homogeneous layer with a free surface--the prototype for conventional hydraulics--the corresponding phenomena in two-layer flows, and a description of the properties of linear waves in stratified fluids in motion. The author applies the aforementioned properties to laboratory and numerical modeling of flow through real complex terrain.