The electronic band structure of the intercalation system Mg(Ti 3S 4) 2 is investigated by a three-dimensional (3D) self-consistent-field (SCF) Hartree-Fock (HF) crystal orbital (CO) approach based on an INDO (intermediate neglect of differential overlap) all-valence Hamiltonian. The band-structure properties of Mg(Ti 3S 4) 2 are correlated with those of the binary matrix as well as the dichalcogenide TiS 2 where the transition-metal is in a higher oxidation-state. The calculated electronic-structure data of Mg(Ti 3S 4) 2 and TiS 2 are compared with available results of experimental measurements. For TiS 2 the present computational findings are furthermore compared with previous band-structure calculations. The formation of charge-density-wave (CDW) solutions in Mg (Ti 3S 4) 2 and Ti 3S 4 are analyzed. The CDW condensation is caused by fluctuating valences (i.e. deviations of an orbital occupancy around its average value) in the Ti sublattice. Some associated many-body effects are discussed. Mg(Ti 3S 4) 2 is a system where electronic and ionic conductivity are both operative. A first-order phase-transition of the insulator-semimetal type is predicted for the ternary system as a function of the spatial localization of the intercalant-atoms in the 1D van der Waals channels. Electronic reorganization-processes between the intercalant and the Ti 3S 4 matrix accompanying this phase-transition are analyzed. It is shown, that the rigid band-model is nonvalid for the interpretation of the band-structure properties of the intercalation compound. The results of frequently used methods in band-structure theory of intercalated transition metal chalcogenides are critically reviewed. The present findings render possible a reinterpretation of some electronic consequences of intercalation. Variations of the one-electron energies in intercalated materials were incorrectly predicted by methods employed conventionally in solid-state theory.