(Almost) Lagrangian fibre bundles arise from completely integrable Hamiltonian systems. Such bundles have local normal forms ("action-angle variables") and have no local invariants. Two global invariants, the monodromy and the Chern class, were identified by Duistermaat. A refinement of the Chern class, now called the Lagrangian class, was found by Dazord and Delzant. In this survey talk I will define these invariants and show how they classify (almost) Lagrangian fibre bundles.
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