It is shown theoretically that the main regularities of spontaneous non-stationary and stationary nucleation on the surface and in the volume of glass are the same. Kinetics of surface nucleation are studied in detail as a function of temperature for the polished surface of cordierite glass. Nucleation occurs mainly on surface defects but spontaneous nucleation on a "perfect" surface takes place simultaneously. The high surface nucleation rate and the high temperature of its maximum T-m(T-m > T-g) is caused mainly by the decrease of the energy barrier Phi* for the critical nucleus.