Explore the intricacies of surface curvature in this comprehensive differential geometry lecture. Delve into various formulas for calculating surface curvature, including those for normal paraboloids, functions passing through the origin, and general conics. Examine practical examples such as spheres, ellipsoids, and the ellipson cubic surface from Rational Trigonometry. Gain insights into the calculation of curvatures for parametric surfaces, following C. F. Gauss's approach. Perfect for mathematics enthusiasts and students looking to deepen their understanding of differential geometry and surface analysis.