The subject of the present diploma thesis is the design of a control system, for the autonomous trajectory tracking of a fixed wing unmanned aerial vehicle (UAV). The first step towards this goal was the proper modelling of all the externally applied forces on the UAV, followed by the derivation of the kinematic and dynamic equations that fully describe the vehicle's motion. Then, a robust flight control system was developed, based on the technique of nonlinear sliding mode control, with the necessary modifications for practical implementation. The navigation problem was solved with the development of a Lyapunov based nonlinear control system, that assures the vehicle's convergence to the desired trajectory. The two control systems were then combined and the closed loop stability was verified through Lyapunov's stability theory. Finally, the model of plausible external disturbances was developed and the total system was tested through a series of simulations. The success of the derived results verifies both the system models and the control techniques that have been applied in the present diploma thesis.