Explore the foundations of universal hyperbolic geometry in this 38-minute video lecture focusing on projective geometry and its connection to Renaissance art. Learn about the 19th-century view of projective space as one-dimensional subspaces of higher-dimensional affine spaces. Examine the projective line and plane, and discover how they relate to perspective rendering in art. Investigate the representation of a circle as a two-dimensional view of a cone, tracing back to ancient Greek concepts. Delve into affine and projective geometry, perspective and points at infinity, and one-dimensional projective geometry. Gain insights into the relationship between affine space and vector space, providing a comprehensive introduction to this important but often overlooked subject in modern mathematics curricula.