Currently, due to the high flow in air traffic, automatic tools for managing the air space become to be important in order to make easy the decision making by the air traffic controlling staff. In this environment, the mathematical optimization is presented as a strong discipline to tackle the different problems involved in the big project known as Air Traffic Management. In this environment, the aircraft collision avoidance takes a prominent place being so much important for a right distribution of the air traffic flow. This book presents two mathematical optimization models based on a geometric construction that allows the conflict detection and resolution. Some algorithmic approaches for problem solving are presented, as well as the results of a broad computational experience with realistic sized instances. The difficulty of the problem together with the need of obtaining a good solution in almost real-time makes the problem an interesting challenge for researching.