Explore the fascinating world of elliptic geometry in this 42-minute video lecture. Discover new laws for spherical and elliptic trigonometry as natural consequences of applying Rational Trigonometry to three-dimensional projective settings. Uncover the remarkable symmetry between spherical and hyperbolic geometries, extending to other geometries as well. Delve into elliptic triangles, projective points, and polar triangles, examining their intimate connection with matrix inverses. Learn about projective quadrance and spread, and master the fundamental laws of elliptic geometry, including the Spread law, Cross law, and Dual cross law. Gain insights into these essential mathematical concepts, suitable for viewers with or without prior knowledge of Rational Trigonometry or the lecture series.