1. Nineteenth-Century Science Breakthroughs in Europe: Historical Background 2. A. F. Möbius: The Time of His Early Life and Academic Education (1790–1815) 3. A. F. Möbius: The Time of His Academic Career (1815–68) 4. During the Napoleonic Wars in Europe: Eyewitnesses and Victims 5. Möbius Strip Topology and More: Elaborations on Mathematics 6. A. F. Möbius and His Time: Elaborations on Astronomy 7. Möbius Strip Topology: Applications from Chemistry 8. The Möbius Strip Topology: Applications from Physics and Nanomaterials 9. Möbius Strip Topology: Highlights from the Arts and Architecture