A theory of optical excitations by using a tight binding model with long-range Coulomb interactions is developed. The model is applied to a C-60 molecule and a cluster, and is treated by the Hartree-Fock approximation followed by a configuration interaction method. Lattice fluctuations are taken into account by a bond disorder model. We first examine what strength of Coulomb interaction is appropriate to describe the electronic structures observed by photo-electron and optical absorption spectroscopy. Then, we demonstrate that the photo-excited states are mainly intramolecular (i.e. Frenkel) excitons with small charge-transfer components. We examine to what extent the dipole forbidden transitions of a single C-60 molecule become dipole-allowed by lattice fluctuations or intermolecular interactions.