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Integrable systems is a category for books that study differential equations and dynamical models admitting exact, often analytic solutions thanks to rich symmetries and many conserved quantities. Covering both classical and quantum settings, these works treat Hamiltonian and Liouville integrability, soliton equations (such as KdV, sine-Gordon, and Toda), Lax pairs, inverse scattering, Painlevé equations, and related tools from symplectic/Poisson geometry, Lie theory, and algebraic geometry. The category spans accessible introductions to advanced monographs, including topics like isomonodromy, the Bethe ansatz, and quantum groups, with applications in fluid dynamics, nonlinear optics, plasma physics, celestial mechanics, and condensed matter. Emphasis is on exact methods, structure-preserving analysis, and rigorous theory.

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