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Hamilton–Jacobi theory is a category for books that present the Hamilton–Jacobi formulation of classical mechanics and its broad mathematical extensions. Titles typically cover the Hamilton–Jacobi partial differential equation, canonical transformations and generating functions, action–angle variables and integrable systems, and links to the calculus of variations and symplectic/Poisson geometry. Many works emphasize applications to celestial mechanics, geometrical optics and wave propagation (eikonal/WKB), optimal control and dynamic programming, and connections to quantum mechanics and semiclassical analysis, with modern developments such as viscosity solutions and weak KAM theory. The category includes introductory texts, advanced monographs, and research collections aimed at advanced undergraduates, graduate students, and researchers, generally assuming background in multivariable calculus, differential equations, and basic mechanics.

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