In this monograph, we study a type of hybrid system that combines a base isolation system with an active control system that applies forces on the base. The control forces are calculated by means of a control law that guarantees an adequate behavior, both of the structure and of the base, considering a wide class of non-linearities of the base isolator and uncertainties in the dynamic model and in the excitation. In order to simulate properly the proposed hybrid system, algorithms are used able to analyze the effect of the base isolation with non-linear behavior. At the same time, it is necessary to have a control law that generates the active control force, whose objective is examined from the point of view of the behavior of the system composed by the structure and the base isolation in purely passive conditions. The control law is formulated for the two subsystems coupled through their boundary conditions. The active control forces are applied upon one of the subsystems in order to guarantee a form of practical stability. In this case, the subsystem over which the control acts is the base and the other subsystem is the structure. In the monograph the equations that describe the two systems of seismic base isolation considered in this monograph are developed (one hysteretic and the other frictional), the use of the hybrid system is justified, the different components are described and a critical analysis of the different existing hybrid systems is performed. The law of adaptive control is developed, the hypotheses are stated and the stability of said law is analyzed. The developed strategy is applied to different buildings with base isolation systems and numerical simulation results of their seismic response are shown.