Explore the fundamental concepts of universal hyperbolic geometry in this 37-minute video lecture. Delve into the projective study of a circle and relativistic geometry, focusing on key topics such as perpendicularity, duality, and the pole-polar correspondence. Learn about the orthocenter of a triangle and discover how quadrance and spread measurements arise from cross ratios. Examine essential formulas including Pythagoras' theorem, Triple quad formula, Pythagoras' dual theorem, Triple spread formula, Spread law, and Cross law. Compare these concepts to their counterparts in Rational Trigonometry and gain insights into the Beltrami-Klein model. Through a structured presentation, grasp the foundations of this geometric framework and its applications in mathematical analysis.