This monograph presents new constructive design methods for boundary stabilization and boundary estimation for several classes of benchmark problems in flow control. It has potential applications to turbulence control, weather forecasting, and plasma control. The basis of the approach used is the recently developed continuous backstepping method. This approach is presented and extended to eliminate one of the well-recognized root causes of transition to turbulence. New results in fluid dynamics and the analysis of Navier-Stokes equations are also presented. This is an excellent reference for a broad, interdisciplinary engineering and mathematics audience. The book may also be used as a supplementary text for graduate courses on control of distributed-parameter systems and on flow control.