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This book provides an introduction to geometric control design methodologies for asymptotic tracking and disturbance rejection of infinite dimensional systems. It also introduces several new control algorithms inspired by geometric invariance and asymptotic attraction for a wide range of dynamical control systems. The book covers the regulation of both linear and nonlinear systems and offers an extensive collection of both types of problems. Examples range from one-dimensional heat and wave equations to control of non-isothermal Boussinesq flows.