Abstarct: So far, the control of robot manipulators in the joint-space has been extensively developed. However, the perfect tracking of robot manipulators in joint space cannot guarantee the perfect tracking of the end-effector in workspace under uncertainties while the aim of control is the desired tracking performance in task-space. Therefore, the robot control in task space under uncertainties is an important subject in the field of robotic research. The model of robot includes both structured and unstructured uncertainties. Thus, in this thesis with an assumption that the Jacobian of robot manipulator is available, the nonlinear control and adaptive control together were used to overcome the model uncertainties. Since some parts of nonlinear dynamics of robot manipulator are known, theses terms can be canceled by feedback linearization. Then, the new controllers such as nonlinear robust controllers, robust adaptive controllers, and adaptive robust controllers are designed to overcome the residual uncertainties. The control design considers some important issues such as the properties of robot dynamics, the bounds of uncertainties, the actuator limits, the constructing cost of robot, and the type of task. Since the Jacobian of manipulator cannot be accurate under uncertainties, the robust nonlinear controls are proposed to control robot with uncertain kinematics and uncertain dynamics. The control approaches are designed baxsed on the sliding mode control, backstepping approach and disturbance observer. We have a challenge with problems such as planning the desired trajectory in the restricted workspace, the limitation of processing time in real time control, and providing the desired performance in implementing stage. In this thesis, the control of two-lixnk elbow manipulator is the case study. The analytical proofs and simulations, confirm the desired performance of controllers.