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Differential geometry as a book category covers the study of geometric structures using the tools of calculus and linear algebra, typically focusing on curves, surfaces and higher-dimensional manifolds equipped with notions such as tangent spaces, metrics, connections, curvature and geodesics. Books in this category range from introductory texts that develop the basics of curves and surfaces and coordinate-free language, to advanced treatments of Riemannian and pseudo-Riemannian geometry, fiber bundles, differential forms and global/topological results like the Gauss-Bonnet theorem. Many volumes emphasize rigorous proofs and abstract theory for mathematics and theoretical physics students, while others take an applied route toward mechanics, relativity, computer graphics, robotics and computer vision. Overall the category serves readers seeking both foundational training in smooth manifolds and tensor calculus and specialized monographs exploring curvature, holonomy, comparison theorems and geometric analysis.

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