<p style='text-indent:20px;'>This paper considers the attitude tracking control problem for a rigid body. In order to avoid the complexity and ambiguity associated with other attitude representations (such as Euler angles or quaternions), the attitude dynamics and the proposed control system are represented globally on special orthogonal groups. An adaptive controller based on a Lie subgroup of SO(3) is developed such that the rigid body can track any given attitude command asymptotically without requiring the exact knowledge of the inertia moment. In the presence of external disturbances, the adaptive controller is enhanced with an additional robust sliding mode term by following the same idea within the framework of SO(3). Finally, simulation results are presented to demonstrate efficiency of the proposed controllers.</p>