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Morse Theory books focus on how the critical points of smooth functions on manifolds encode and reveal a space’s global topological and geometric structure. This category includes accessible introductions for advanced undergraduates and graduate students as well as research monographs, covering core topics such as critical points and indices, gradient flows, handle decompositions, and the computation of homology via Morse inequalities. It also spans extensions and applications—Morse–Bott theory, discrete and computational Morse theory for combinatorics and algorithms, and links to Riemannian geometry, symplectic topology, dynamical systems, and topological data analysis. Typical prerequisites are multivariable calculus and some differential geometry or algebraic topology, and titles range from conceptual overviews and lecture notes to problem-driven texts and comprehensive references.

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