This text is an introduction to the feedback control of lightly damped flexible structures, the emphasis is placed on basic issues such as actuator and sensor selection, placement and dynamics, and actual implementation for solving practical problems. The book consists of 11 chapters, in chapters 2 to 5, the open-loop transfer functions of various active structures are derived from their constitutive equations, the discussion includes a truss and sandwich beams and plates with embedded piezoelectric actuators and sensors. The virtues of collocated actuator-sensor configurations are pointed out and used to develop active damping with guaranteed stability. Chapters 6 to 8 are devoted to the model-based control of SISO systems, optimal control is developed graphically using the symmetric root locus, the gain-phase relationship is discussed and the design tradeoffs are explained in the frequency domain. The issues of robustness with respect to the parametric uncertainty and the spillover instability are examined. After two short chapters on controllability (ch. 9) and stability (ch. 10), the book concludes with a set of applications to active damping and precision positioning of a set of aerospace, mechanical and civil engineering structures. The book is intended for structural engineers who want to acquire some background in vibration control, it can be used as a textbook for a graduate course on vibration control or active structures. The text is supplemented with 98 problems.