In this dissertation, planar energy optimal waypoint guidance synthesis for an unmanned aerial vehicle is proposed. It is shown that a trajectory passing through all the waypoints, obtained by applying optimal guidance laws, is optimal if boundary conditions at waypoints are properly determined. The proposed optimal waypoint guidance is synthesized in two steps: the sub-optimal boundary conditions are calculated first, and then an optimal guidance law is applied to guide the vehicle between two adjacent waypoints. For a lag-free vehicle, the optimal guidance law with impact angle constraint is used as the waypoint guidance law. In this case, the required boundary conditions are the waypoint pass angles, the flight path angles at waypoints. Using the analytic time solution of the optimal guidance law, the energy cost for entire trajectory is given by a quadratic function of the waypoint pass angles. By differentiating the energy cost by the waypoint pass angles, simple linear algebraic equations to calculate the sub-optimal waypoint pass angles are derived. Therefore, the proposed waypoint guidance synthesis makes it possible to generate the energy optimal trajectory passing through all the waypoints in real time. If the vehicle is represented by a 1st-order lag system, lateral acceleration is newly added to the boundary conditions. Hence, the optimal guidance law with terminal constraints on impact angle and acceleration is required for waypoint guidance. Since the closed-form trajectory solution for the law is not available, the optimal waypoint pass angles and accelerations are determined by a parameter optimization technique. Although the proposed synthesis does not produce the optimal trajectory in real time, it can greatly reduce the computation time compared with the original trajectory optimization.