We associate, to a Lagrangian submanifold L L of a symplectic manifold, a new homology, called the cluster homology of L L , which is invariant up to ambient symplectic diffeomorphisms. We discuss various applications concerning analytical, topological, and dynamical properties of Lagrangian submanifolds. We also deduce a new universal Floer homology, defined without obstruction, for pairs of Lagrangian submanifolds.
