This book addresses and answers essential questions of elementary geometry on the surface of a sphere and their applications to the Earth and celestial sphere (mathematical geography and astronomy) in a way that provides background knowledge for a reality-based geometry education in secondary schools. The focus is on everyday phenomena such as geographic coordinates, compass, shortest paths, solar movement, time, and world maps, allowing students to learn mathematics in the sense of Freudenthal—not as applied mathematics, but as a way to apply mathematics. Reflections on modeling and historical aspects complement the discussions. The theory is developed only to the extent necessary for these goals. Digital tools are used where they appear necessary and sensible. Each chapter offers a rich collection of exercises.