In this thesis, the design of a new class of control systems, called Fault Tolerant Control Systems (FTCS), has been studied thoroughly. Fault Tolerant Control Systems are closed-loop control systems which can tolerate system component faults or failures and maintain the system stability and a certain degree of performance. FTCS are extremely important in safety-critical applications. In this thesis, the system model with component faults is first formulated mathematically. Important issues in FTCS, such as redundancy, performance degradation, and time constraints are explored in depth. The definitions of actuator and sensor redundancy are first introduced and then clearly elaborated. Based on how the system redundancy is utilized, FTCS can be classified into active FTCS and passive FTCS. With a better understanding of the characteristics of both types of FTCS, the problems of designing such systems are investigated in a unified framework. Existing design methodologies are reviewed. New design approaches for passive FTCS protecting against actuator/sensor failures are proposed. The proposed methods have effectively utilized actuator redundancy and sensor redundancy in the design to achieve the fault tolerance. For active Fault Tolerant Control Systems, Fault Detection and Identification (FDI) schemes are introduced first and two common design techniques based on state estimation and parameter estimation are compared. The comparison is mainly based on the fault detection rate and availability of the fault information. By taking into account the integration of FDI and reconfigurable control, a new bounding parameter estimation based fault identification scheme is proposed followed by an applicable reconfigurable control scheme. The integrated design of FDI and reconfigurable control is thus achieved. Three design examples are presented to demonstrate the effectiveness of the proposed design methods for both passive and active FTCS. The main contribution of this thesis is that new design methodologies for both passive and active FTCS are developed, the important concept of system redundancy are incorporated in the proposed design. In addition, many important issues of FTCS are first explored in this thesis.