Active vibration control of civil engineering structures for earthquake protection is a widely researched area attracting interest from structural and control engineers. This book is intended for both areas. It gives an overview of existing structural control methods and technologies including passive, active, semi-active and hybrid control. It also introduces the fundamentals of structural dynamics and control systems design. An extensive analysis of a frame-pendulum model is analysed resembling a tuned mass damper including inelastic stiffness degradation. LQG and H-infinity multiobjective active control schemes are designed and evaluated. A novel design method is proposed for minimising peak responses in discrete-time, incorporating constraints on the magnitude and rate of the control signal solved via linear programming methods. The problem of stiffness matrix estimation from experimental data is formulated as an optimisation problem and solved via an alternating convex projection both static and dynamic. The method is incorporated in an adaptive control scheme involving the real-time redesign of an LQR active vibration controller when there is stiffness uncertainty.