Adami R., Dell'Antonio G., Figari R., Teta A. The Cauchy Problem for the Schroedinger Equation in Dimension Three with Concentrated Nonlinearity (66K, LATeX 2e) ABSTRACT. We consider the Schroedinger equation in R^3 with nonlinearity concentrated in a finite set of points. We formulate the problem in the space of finite energy V, which is strictly larger than the standard H^1-space due to the specific singularity exhibited by the solutions. We prove local existence and, for a repulsive or weakly attractive nonlinearity, also global existence of the solutions.