The structural and photophysical characteristics of MAPbBr3 single crystals prepared using the inverse temperature crystallization method are evaluated using temperature-dependent X-ray diffraction (XRD) and optical spectroscopy. Contrary to previous research reports on perovskite materials, we study phase transitions in crystal lattice structures accompanied with changes in optical properties expand throughout a wide temperature range of 300-1.5 K. The XRD studies reveal several phase transitions occurred at ~210 K, ~145 K, and ~80 K, respectively. The coexistence of two different crystallographic phases was observed at a temperature below 145 K. The emission peaks in the PL spectra are all asymmetric in line shape with weak and broad shoulders near the absorption edges, which are attributed to the Br atom vacancy on the surface of the crystals. The time-resolved PL measurements reveal the effect of the desorption/adsorption of gas molecules on the crystal surface on the PL lifetimes. Raman spectroscopy results indicate the strong interplays between cations and different halide atoms. Lastly, no diamagnetic shift or split in emission peaks can be observed in the magneto-PL spectra even at an applied magnetic field up to 5 T and at a temperature as low as 1.5 K.