Explore key concepts in universal hyperbolic geometry through this comprehensive 43-minute video lecture. Delve into the properties of right triangles, including singly, doubly, and triply right configurations. Learn about Thales' theorem and its relationship to Euclidean right triangles, with a focus on the spread as a crucial ratio. Discover the significance of quadrea in triangle analysis and master Napier's rules for solving right triangles. Follow along with proofs, engage in suggested exercises, and gain a deeper understanding of how to approach problems by creating right triangles. This lecture provides a solid foundation in advanced geometric concepts, blending theoretical knowledge with practical problem-solving techniques.