This thesis is dedicated to solve the adaptive control problems of robot in the presence of all uncertainties in the kinematics, manipulator dynamics and actuator dynamics. The main contribution of the thesis is that a novel adaptive regressor design method is proposed which enables the adaptation of different kinds of uncertainties simultaneously during the control process. Based on the novel regressor design, adaptive control methods have been proposed for regulation and tracking control of robot with uncertain kinematics, manipulator and actuator dynamics. These approaches constitute the first results in the research area of robot control to deal with both kinematic and actuator dynamic uncertainties. Through Lyapunov analysis, the stability of the closed-loop systems are shown to be guaranteed and the sufficient conditions to be satisfied are explicitly presented. The proposed control schemes have all been examined through simulation studies to confirm their effectiveness in dealing with the kinematic and dynamic uncertainties. Experiments were also conducted based on a vertical two-link robot driven by motors with current amplifiers.