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Riemannian geometry (as a book category) encompasses works about the study of smooth manifolds equipped with Riemannian metrics and the geometric, analytic, and topological consequences of curvature. Titles range from introductory textbooks that develop geodesics, Levi-Civita connection, sectional/Ricci/scalar curvature, and comparison theorems, to advanced monographs treating global results, geometric analysis (eigenvalues, heat kernel, Ricci flow), synthetic and metric-generalizations, and detailed examples (spheres, hyperbolic space, Einstein manifolds). Books in the category include lecture notes, problem collections, and research surveys aimed at advanced undergraduates, graduate students, and researchers, typically assuming multivariable calculus, linear algebra, basic topology, and some manifold theory; many also emphasize applications to topology, general relativity, and mathematical physics.

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