First principles LAPW and semiempirical EHT methodology is used to characterize the bonding in LiTi2O4 (spinel) and LiTiO2 (trigonal) as well as the corresponding Li-extracted TiO2 structures. In optimized structures, the Ti-Ti distance indicates that the spinel structure is most stable, in agreement with experimental observations. Deintercalated compounds of both structures are broad-band insulators with a gap of similar to 2 eV. Upon intercalation of Li both structures become conductors with the Fermi level situated within the d band. The intercalation causes no pronounced changes of the DOS of cubic spinels. On the contrary, trigonal compounds show considerable rearrangement of energy states at the bottom of the d band. Both, density of states and difference density plots show that the host framework of TiO2 oxide becomes more ionic with intercalation of Li, The interaction scheme constructed for spinel structures shows that electron density originating from intercalated Li atoms can be placed only on Ti atoms, which is confirmed by electron density plots. The difference density plots constructed for Li electron density only show that the occupation of d states due to the intercalation creates Ti-Ti (t(2g)-t(2g)) bonds in a more effective manner in the spinel than in the trigonal structure. This 3D t(2g) band is the electronic prerequisite for the superconductivity of the spinel LiTi2O4 compounds.