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KAM theory is a specialized category in mathematics and mathematical physics centered on the Kolmogorov–Arnold–Moser results about the stability of quasi-periodic motion in nearly integrable Hamiltonian systems. Books in this category address the persistence and breakdown of invariant tori under small perturbations, small-divisor methods, action–angle variables, and related tools from dynamical systems and symplectic geometry. The category includes graduate textbooks, research monographs, and expository volumes, often covering extensions such as Nekhoroshev and Aubry–Mather theory and applications to celestial mechanics, plasma and accelerator physics, and nonlinear waves. It is aimed at advanced students and researchers seeking rigorous treatments of stability and the onset of chaos in Hamiltonian dynamics.

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