Like other systems, robot control systems are subject to external disturbances, uncertainty in system parameters and unmodeled dynamics. These usually reduce the stability and performance of the system. A problematic issue in robot control is existence of structured and unstructured uncertainties in the dynamic model of the robot. Furthermore, in many applications such as welding and cutting, the robot manipulator is in contact with its surrounding environment to exert a force on it. Sometimes this force is required to be controlled; therefore, force control plays a significant role in accomplishing the work. Robot force control is an active field of research in robot control, and numerous control schemes have been developed in recent decades. One of the simplest methods among these control methods is hybrid force/position control, in which, using a selection matrix, workspace is divided into two orthogonal suaces: position suace and force suace. So far, many studies have been conducted using this force control method. However, it is sometimes difficult to obtain precise information regarding to environment geometry for applying force control needed to determine the selection matrix. Another force control algorithm is impedance control. The aim of this method is to control the mechanical impedance of the manipulator and environment, rather than control the position or force in isolation. Furthermore, impedance control does not require the switching control required in hybrid control. Thus, impedance control can be promising force control scheme for some applications. In the concept of impedance control, the controller must be designed in such a way that regulates the dynamic behavior between the motion of the manipulator and the force exerted on the environment. This desired dynamic behavior is referred to as the target impedance. The target impedance of the manipulator is often specified by a second-order dynamics that mimics a mass-spring-damper system. In this thesis, we develop two robust impedance control schemes for robot manipulators. With the proposed schemes, the robot can track the specified desired force in the presence of uncertainties in its dynamic model. Furthermore, these schemes are designed such that they reduce chattering phenomenon in the exerted force to the environment. Convergence and uniform global asymptotic stability of control systems are analyzed and guaranteed using Lyapunov stability theory. Simulations are performed on a two-link robot manipulator, in which the dimensions and masses of links are considered equal to those of the shoulder and elbow of the TA9 industrial robot manipulator. Comparing simulation results of the proposed schemes with some other approaches indicate that position and force tracking errors are more reduced and the control systems are more robust to uncertainty in the robot dynamic model. Keywords: Uncertainty, Robust Control, Impedance Control, Chattering Phenomenon, Lyapunov Stability Theory, TA9 Industrial Robot Manipulator