In this thesis the problem of spacecraft attitude control is investigated. The spacecraft dynamics are modeled as a rigid body system controlled by 4 thrusters, and the kinematics are represented by direction cosine matrix. In this thesis, the effectiveness of retrospective cost adaptive control for spacecraft attitude control is evaluated. The prominent feature of this adaptive controller is that it requires little knowledge of the system to be controlled. This makes this controller attractive since for most spacecraft knowledge of the spacecraft’s inertia tensor is limited and will sometimes change over the spacecraft lifetime.