[en] A theory is developed to describe the excitation of the diatomic carbon moelcule in interstellar clouds. The probabilities of quadrupole transitions within the ground state and of intercombination transitions between levels of the lowest triplet and singlet states are computed. The populations of excited rotational levels can be used as a diagnostic probe of local temperature, density, and strength of the radiation field, although all three parameters cannot usually be determined from C² data alone. Calculated rotational populations are presented for a range of physical conditions and are used to interpret existing interstellar absorption line observations of C². Because of the competition between radiative and collisional excitation processes, the rotational excitation temperature tends not to be a good measure of kinetic temperature. An unusual radio frequency spectrum of C² is predicted