Integrable Systems in the realm of Algebraic Geometry

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Introduction.- Integrable Hamiltonian systems on affine Poisson varietie: Affine Poisson varieties and their morphisms Integrable Hamiltonian systems and their morphisms Integrable Hamiltonian systems on other spaces.- Integrable Hamiltonian systems and symmetric products of curves: The systems and their integrability The geometry of the level manifolds .- Interludium: the geometry of Abelian varieties: Divisors and line bundles Abelian varieties Jacobi varieties Abelian surfaces of type (1,4).- Algebraic completely integrable Hamiltonian systems: A.c.i. systems Painlev analysis for a.c.i. systems The linearization of two-dimensional a.c.i. systems Lax equations.- The Mumford systems: Genesis Multi-Hamiltonian structure and symmetries The odd and the even Mumford systems The general case .- Two-dimensional a.c.i. systems and applications: The genus two Mumford systems Application: generalized Kummersurfaces The Garnier potential An integrable geodesic flow on SO(4) ...