Global Positioning System (GPS) is an all-weather 24-hour globally available positioning system. Because of its high availability and supreme accuracy, it has been widely used in navigation, surveying, constructions, public services, military, space, and other areas. In this presentation, the positioning method of GPS is introduced. Three segments of GPS, the spacecraft, the ground control system and the user equipment, and their functions are discussed. GPS measurements and error sources are presented in details since they are critical in designing any GPS application systems. During the last two decades of GPS utilization, methods have been developed to extend the GPS capability to meet the requirements of various systems. These systems include millimeter accuracy survey system, high availability vehicle guidance and tracking system, and one out of a billion error probability high integrity aircraft landing system. Methods to achieve these applications are presented. Finally, the mathematical problems we encountered in designing an aircraft landing system are brought up for discussions.