The theory of the excitation of nuclei by electrons of intermediate energy has been studied. Cross sections for the excitation of nuclei due to the interaction of the electromagnetic field of the electron with the electric dipole, qua-drupole, and with the magnetic dipole and quadrupole moments of the nucleus have been evaluated explicitly in terms of these moments.A relationship between the electro-excitation cross section and corresponding X-ray excitation cross section is established. This relationship is independent of all properties of the nucleus except for the change in the energy, angular momentum and parity involved in the transition.The predictions of the theory are compared with the experimental measurements in the excitation of In115. It is found that no definite information about the nuclear levels is obtained by this comparison because of insufficient precise experimental results. Measurements which would lead to information about the properties of the nuclear states are suggested.