wikipedia Integrable system - Wikipediabook Olivier Babelon, Denis Bernard, Michel Talon - Introduction to Classical Integrable Systemsnotes An Introduction to Gauge Theory and its Applications connects vector bundles, Yang-Mills in 4 dimensions, topology of smooth 4-manifolds, algebraic geometry of stable holomorphic bundles and Hitchin integrable systemsarticle How to count curves? - Ian Strachanbook Integrable systems twistors, loop groups and Riemann surfaces 
lecture notes and problems Integrable systems (Math 99r, Spring 2024) - Sanath Devalapurkarreferences Mathematical Retreat on Integrable Systemsreferences Some recent books on symmetries, integrability and all that (1999-2004)lecture videos Short course on Hitchin Integrable Systems, 1st lecture. Tom Sutherland (Lisbon University). - YouTubebook E Markman, “Spectral curves and integrable systems”book J Hurtibuse, “Separating coordinates for the generalized Hitchin systems and the classical r-matrices”book A Gorsky, N Nekrasov, V Rubtsov, “Hilbert Schemes, Separated Variables, and D-Branes”talk video A tale of supersymmetry: The dark magic of integrable systems - YouTube with slides following paper Seiberg-Witten integrable systems