More than 70% of the earth is covered by seas and oceans that are vast and valuable resources of the earth. Seas play important role in strategic, military, political and economic issues. Due to difficulty and high cost of research and activity in underwater environments, using of underwater robots is useful in these areas. Among these robots, autonomous underwater vehicles (AUVs) are popular. Today's these robots are used in various commercial, military and scientific applications. Nonlinear dynamics, structural and nonstructural uncertainty and external disturbances has caused challenges for control of these robots. Therefore by use of an adaptive control system that is robust with respect to external disturbances can be overcome these challenges. In this project the mathematical model of an AUV described and then two control systems are proposed for this model. First an adaptive robust control scheme for six-degree of freedom of AUV is expressed that by using two different adaptation laws, parameters of the systems and bound of the disturbances vector are estimated and are used in the control law. Since linear velocities of underwater robots are often unavailable, these velocities are estimated by extended Kalman filter (EKF). In this project, EKF is applied to simplified model of vehicle. In second section of the project, the model of AUV is divided into horizontal and vertical planes, and an adaptive controller is proposed in these two planes to control depth and heading of the AUV. If vehicle has roll, model of AUV can not be separated into these two planes. Thus in this thesis by using some transformation roll of the vehicle is damped. In the following, stability of both controllers is proven by using Lyapunov theory and Barbalat's lemma. Finally, the proposed control systems are simulated in six-degree of freedom model of the AUV which represent that the controllers are robust with respect to measurement noise, external disturbances and uncertainty in the model. Keywords: autonomous underwater vehicle, robust adaptive control, external disturbance estimation