Presents the results of electronic structure calculations for first and second stages of lithium intercalated graphite (LiC6 and LiC 12). Results for LiC6 have been presented earlier by Holzwarth et al. using a modified KKR method. The authors results are in good qualitative agreement with theirs for LiC6. To elucidate electronic structures of several stages of intercalation, they have studied various modifications of graphite and also present results for some useful hypothetical unit cells. All the authors calculations have been performed within the framework of the extended tight binding (LCAO) method with the Gaussian basis set. From detailed calculations of densities of states, they conclude that Li-2s electrons are transferred into carbon pi bands. This results in shifting the Fermi level into the region of high density of states (compared to pure graphite) and thus to increased conductivity. The calculated density of states at the Fermi level for LiC6 and LiC12 is 0.25 and 0.12/(eV C atom), respectively. Recall that for pure graphite this number is nearly equal to zero. The authors have computed the Fermi surface extremal orbits and present data for these orbits to be compared with, e.g. cyclotron experiments. Important differences are found in Fermi surfaces of stage-1 and stage-2 compounds. The authors also show that a first principle quasi-two-dimensional Harrison construction can predict and explain the shape of the Fermi surfaces for intercalated graphite compounds. The calculations also tend to support the rigid band model idea which has been proposed in the literature.