A systematic investigation on the neutral and anionic digallium tetraoxide, Ga2O4 has been carried out by using density functional theory (DFT), second-order Moller-Plesset perturbation theory (MP2), and the coupled cluster approach with single and double substitutions and a perturbative treatment of the triple excitations [CCSD(T)]. The geometry of neutral Ga2O4 has been proposed earlier, from an experimental study, to adopt a D-2d symmetry (J. Phys. Chem. 1979, 83, 656). However, the current research reveals that, out of the several isomers considered for neutral and anionic digallium tetraoxide, the B-3(1u) and B-2(3g) of the planar D-2h geometry (7a-D-2h) are the lowest-energy states for Ga2O4 and Ga2O4-. Our computations rule out the D-2d geometry (3-D-2d) as a viable contender for neutral Ga2O4. The B-3(2) (3-D-2d) state is located above the B-3(1u) (7-D-2h) state by at least 4.26 eV. The energies of the low lying states, geometrical parameters, and energetic features (VEDE, AEDE, and AEA) are reported. The AEA of Ga2O4 is calculated to be 3.94 eV (B3LYP), 3.24 eV (MP2), 3.42 eV [CCSD(T)//B3LYP], and 3.38 eV [CCSD(T)//MP2], respectively. In addition, the dissociation energy, D(sic) for the process Ga2O4 (B-3(1u)) -> 2GaO(2) ((2)A(2)) is 3.59 eV (B3LYP), 5.08 eV (MP2), 4.82 eV [CCSD(T)//B3LYP], and 4.80 eV [CCSD(T)//MP2]. The results obtained in this work are critically analyzed, discussed, and compared with those of the analogous metal oxides.