Exciton binding energy and excited states in monolayers of tungsten diselenide (WSe(2)) are investigated using the combined linear absorption and two-photon photoluminescence excitation spectroscopy. The exciton binding energy is determined to be 0.37 eV, which is about an order of magnitude larger than that in III-V semiconductor quantum wells and renders the exciton excited states observable even at room temperature. The exciton excitation spectrum with both experimentally determined one- and two-photon active states is distinct from the simple two-dimensional (2D) hydrogenic model. This result reveals significantly reduced and nonlocal dielectric screening of Coulomb interactions in 2D semiconductors. The observed large exciton binding energy will also have a significant impact on next-generation photonics and optoelectronics applications based on 2D atomic crystals.