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The paper presents the transmission spectra of hybrid perovskite MAPbI3 single crystals near the fundamental absorption edge in a wide temperature range. The absorption coefficient α of the single crystal samples is estimated at a temperature T = 150 K for the light with a photon energy E = 1.6 eV and at T = 40 K for E = 1.8 eV. The obtained values turned out to be several orders of magnitude smaller than the values of α for thin-film samples known from the literature. A sharp shift of the fundamental absorption edge by ~ 100 meV was observed at a temperature T1 = 160 K of the structural phase transition from the tetragonal to the orthorhombic phase. The temperature hysteresis of the shift of the fundamental absorption edge near T1 was recorded, which is characteristic of a first-order phase transition.