This graduate-level course examines the physical processes underlying the movement and dilution of substances traveling in rivers, lakes, the oceans. We start with the concept of 1-D Fickian diffusion (Brownian motion) and gradually expand our analysis to steady shear flow dispersion in rivers and streams. Additional topics include unsteady dispersion (e.g. oscillatory shear flows), coastal dispersion, offshore dispersion, vertical mixing in stratified waters, and the flushing of basins.