Explore the fundamental concepts of two-dimensional surfaces, focusing on the sphere, in this third lecture of a beginner's course on Algebraic Topology. Discover various ways the sphere appears, including as a Euclidean sphere, and its relationship to stereographic projection and the inversive plane. Delve into topics such as line segments, theory of links, rational number lines, and inversion. Learn from Associate Professor N J Wildberger of the School of Mathematics and Statistics at UNSW in this 42-minute video that builds upon the foundation laid in previous lectures on planar surfaces.