Optimal control of fluid dynamics is of fundamental importance in aero/hydrodynamic vehicles, combustion control in engines, fire suppression, magnetic fusion, and ocean and atmospheric prediction. This book provides a well-crystalized theory and computational methods for this new field. It is the first and only book to provide a focused presentation of the issues concerning feedback control in viscous hydrodynamics. Engineers, physicists, and mathematicians working in the aforementioned fields will be interested in this book.