I will give a report on a joint work with Kenji Fukaya, Yong-Geun Oh and Hiroshi Ohta. We defined obstruction classses for defining Floer homology for Lagrangian intersection and constructed Floer homology when all the obstruction classes vanish. In fact, this construction depends on several additional choices. We also constructed what we call a filtered A∞-algebra associated to a Lagrangian submanifold, in which obstruction classes are formulated. Dependence on additional choices is also controlled in terms of this algebra. (In this work, Lagrangian submanifolds are assumed to be “relatively spin”.)