We study the collision avoidance between two aircraft flying in the same vertical plane: a host aircraft on a glide path and an intruder aircraft on a horizontal trajectory below that of the host aircraft and heading in the opposite direction. Assuming that the intruder aircraft is uncooperative, the host aircraft executes an optimal abort landing maneuver: it applies maximum thrust setting and maximum angle of attack lifting the flight path over the original path, thereby increasing the timewise minimum distance between the two aircraft and, in this way, avoiding the potential collision. In the presence of weak constraints on the aircraft and/or the environment, the angle of attack must be brought to the maximum value and kept there until the maximin point is reached. On the other hand, in the presence of strong constraints on the aircraft and the environment, desaturation of the angle of attack might have to take place before the maximin point is reached. This thesis includes four parts. In the first part, after an introduction and review of the available literature, we reformulate and solve the one-subarc Chebyshev maximin problem as a two-subarc Bolza-Pontryagin problem in which the avoidance and the recovery maneuvers are treated simultaneously. In the second part, we develop a guidance scheme (gamma guidance) capable of approximating the optimal trajectory in real time. In the third part, we present the algorithms employed to solve the one-subarc and two-subarc problems. In the fourth part, we decompose the two-subarc Bolza-Pontryagin problem into two one-subarc problems: the avoidance problem and the recovery problem, to be solved in sequence; remarkably, for problems where the ratio of total maneuver time to avoidance time is sufficiently large (≥5), this simplified procedure predicts accurately the location of the maximin point as well as the maximin distance.