We present the first ab initio all-electron local-density-functional study of the electronic structure of the TiC(001) surface, using the full-potential linearized-augmented-plane-wave method for a five-layer slab. Near the edge of the film Brillouin zone, surface states and surface resonance states of C 2s and of C 2p--Ti 3d character are found to be split off and shifted to smaller binding energies by about 0.5 eV. Accordingly, the surface C 2s-- and C 2p--like densities of states are shifted by the same amount as compared with the bulk like interior of the film. A small surface-induced peak of Ti 3d--derived states is found just at the Fermi energy. The absence of any significant surface-induced core-level shift for the C 1s states demonstrates that the formation of TiC(001) surface states is not due to an overall electrostatic shift in the potential of the surface C atoms, but is explained by the change of bonding at the surface. This is shown for the C 2s--like states: Their charge density exhibits a notable deformation (inward polarization) at the surface. The calculated work function is found to be 4.70 eV for the stoichiometric surface, which is, as expected, larger than the experimental value of 3.8 eV reported for a TiC(001) surface containing about 6% surface carbon vacancies. The electronic charge density in the vacuum region is higher above the C atoms than above the Ti atoms due to the transfer of about 0.3 of an electronic charge from the metal to the nonmetal.