Luminescence, transmission, reflection, and wavelength modulation transmission and wavelength modulation reflection spectra of HgGaInS4 crystals were researched in the temperature range of 300-10 K. This article discusses the various features observed in the spectra of HgGaInS4 crystals. The dependence on temperature of the energy gap is shown. Spectra of wavelength modulation transmission have minima a1, a2, and a3, which vary with temperature and are caused by indirect transitions L-Г with phonon absorption and emission. Spectra of thicker crystals have more features caused by the same indirect transitions. The photoluminescence show a strong maximum at 2.43 eV, attributed to radiative recombination of free excitons. These various features have significant implications for the understanding of the electronic and optical properties of HgGaInS4 crystals.