This thesis concerns the recently developed control method known as L_1 Adaptive Control, and recognizes its potential in the field of aircraft control. It starts by outlining the essential theory required to complete this thesis, before introducing two different L_1 control schemes which also have been used to address the given control problem. Two linearized mathematical models of an aircraft’s longitudinal and lateral dynamics form the basis for the control problem, and these are further defined by aerodynamic data provided by KDS. The first control scheme is designed to compensate for unknown matched parameter uncertainties and is applied to the longitudinal model where the pitch angle is the state to be controlled. The simulation results will show that despite uncertainties imposed on the system and sudden changes in the model dynamics, the controlled system response shows uniform performance.In the second scheme the presence of matched time-varying uncertainties, bounded time-varying disturbances and unknown actuator efficiency is considered. These unknown elements may represent the varying conditions experienced by an aircraft during its flight operation. This scheme is applied to both the longitudinal and lateral models where the pitch, yaw and roll angles are the states to be controlled. Furthermore the performance is benchmarked against a PID controller and the results clearly show the L_1 adaptive controller to be a far more robust solution to the control problem.In the last simulation, the longitudinal inner loop control model is augmented with an outer loop positional control design, represented by a PID controller. This simulation shows that despite the time-varying reference input the L_1inner loop controller shows uniform tracking behavior.