2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159496This survey examines separation of variables for algebraically integrable Hamiltonian systems whose tori are Jacobians of Riemann surfaces. For these cases there is a natural class of systems which admit separations in a nice geometric sense. This class includes many of the well-known cases.This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/Mathematical PhysicsAlgebraic GeometryExactly Solvable and Integrable Systemstext