Calculations have been performed in a study of the electronic structure of the truncated icosahedral C60-"Buckminsterfullerene" or "follene-60" and intercalated compounds of C60 with alkali atoms within the local density approximation. Certain carbon-carbon bond lengths were assumed and the evaluated molecular eigenvalues were found to be rather insensitive to small changes in the carbon-carbon bond lengths. Theoretical ionization potentials and electron affinities calculated with the von Barth-Hedin exchange-correlation potential for C60 were found to be in good agreement with available experimental data, which was not the case when using the X-alpha-exchange potential with alpha = 0.7. Encouraged by this agreement between theoretical and experimental data, calculations were performed for alkali-containing compounds MC60, where M = Li, Na, K, Rb, Cs and K2C60 and the evaluated ionization energies were used for the identification of the locations of the alkali atoms. The electronic structure of these carbon- and metal-containing clusters was also analyzed by means of a Mulliken charge density analysis, a partial density of state analysis and contour plots of the electronic charge density of the valence levels. Energies of optical transitions were evaluated and compared with available experimental data and with predictions from other calculations.