Explore the fundamental concepts of projective geometry in this 22-minute video lecture from the Universal Hyperbolic Geometry series. Delve into Pappus' theorem, the cornerstone of projective geometry, and understand the crucial concept of cross ratio for points on a line and concurrent lines. Learn about the Cross ratio theorem, which demonstrates the invariance of cross ratio under projection, and Chasles theorem for points on a conic. Examine the applications of these principles in hyperbolic geometry and gain insights into the work of Pappus of Alexandria. Practice with exercises to verify Pappus' theorem in special cases and develop a deeper understanding of cross ratio transformations. Conclude by exploring the connections between projective geometry and Desargues' theorem, providing a comprehensive overview of these fundamental geometric concepts.