Polymorphism in barium gallate BaGa2O4 was studied using electron diffraction and high resolution electron microscopy. Three modifications of BaGa2O4 with structures closely related to the high-temperature α-form were observed. The phase transitions from γ-BaGa2O4 (aγ = 18.6143(2)Å = 2√3aα, cγ = 8.6544(1) Å = cα, S.G. P63) to β-BaGa2O4 (aβ = 2aα, Cβ = cα S.G. P6 3) and to the new δ-polymorph having a monoclinic structure (aδ = cα, bδ = 2a α + bα, cδ = 2b α and β ≈ 92°, S.G. P21/c) were induced by electron beam irradiation. High resolution electron microscopy (HREM) observations allow to establish the close similarity between the structures of δ-BaGa2O4 and β-SrGa2O4. The γ→β and β-δ transitions involve a rearrangement of oxygen atoms in the BaO layers together with a tilting distortion of the tetrahedral framework. The microstructure of the δ-phase is characterised by the presence of numerous translation and orientation domains.