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Using the first principles full-potential linearized augmented plane-wave method within the local density approximation, we have studied the structural, electronic and optical properties of Ga 2 O 3 in its ambient, monoclinic (β) and high-pressure hexagonal (α) phases. It is found the both β-Ga 2 O 3 and α-Ga 2 O 3 have an indirect band gap. The conduction band minimum (CBM) is located at Γ point for both phases, whereas the valence band maximum (VBM) is located at the M point for β-Ga 2 O 3 and at L point for α-Ga 2 O 3 . The calculated total and partial density of states are also presented. The analysis of the electron charge density shows that the Ga–O bonds have significant ionic character. The anisotropic optical properties are investigated by means of the complex dielectric function, which are explained by the selection rule of the band-to-band transitions. For the monoclinic phase, it is shown that the component with y -direction are more pronounced than that along the x and z .