Continue exploring fundamental formulas for curvature of surfaces in three-dimensional space defined by algebraic equations. Delve deeper into the concept that the normal paraboloid at a point on such a surface encodes key quadratic metrical information, including curvatures. Expand on previous discussions to address the general case, moving beyond situations where the tangent plane is horizontal. This 36-minute lecture builds upon earlier material in the Differential Geometry series, providing advanced insights into the mathematical analysis of curved surfaces.