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Angular Excess, Girard's Theorem, and Geodesics in Differential Geometry Curvature and Parameterized Curves in Differential Geometry Comparing Differential Geometry and Topology Differentiable Manifolds and Riemannian Metrics in Differential Geometry Embeddings in differential topology Hyperbolic and elliptic geometries (general) and generalizations Implicit and Parametric Definitions of a Curve in Differential Geometry Definition, Motivation, and Historical Development of Differential Geometry Manifolds and Orientable Surfaces in Differential Geometry The Historical Development of Differential Geometry and Non-Euclidean Geometry Coordinate Systems in Differential Geometry Describing Curves with Implicit Equations and Level Sets in Differential Geometry History of Differential Geometry Calculating the Speed of a Curve in Differential Geometry Parameterizing Curves and Computing Arc Length in Differential Geometry Velocity Vectors and Tangent Lines of the Astroid Curve in Differential Geometry Manifolds and Diffeomorphisms in Differential Geometry Parameterizing Curves with Circles and Parabolas in Differential Geometry