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.