This thesis develops an output-tracking controller to control the end-effector pose of an $N$-link free-floating space manipulator, with non-zero momentum. The space manipulator is modelled as an open-chain multi-body system with multi-DOF joints, and its kinematics and dynamics are derived on the Special Euclidean group $\SE$. Using the conservation of linear and angular momentum of the system, the dynamics of the space manipulator is carefully reduced. The input-output linearization of the system is performed on the Lie algebra $\se$, without adopting any local coordinate chart for the $\SE$. Coordinate-free pose and velocity error functions on $\SE$ are then employed to define a modified feedforward, feedback PID control law to stabilize the end-effector pose to a feasible trajectory. Simulation examples are provided to demonstrate the tracking capabilities of the proposed controller.