HgGa2Se4 crystals belong to the HgGa2X4 (X = S, Se, Te) compounds and crystallize in a classical chalcopyrite structure. An investigation of such materials as HgGa2Se4 is of interest since they possess linear and nonlinear optical properties and a wide band gap (2.2 - 2.6 eV) [1]. The active elements and different devices whose properties based on nonlinear optical effects are developed basing on HgGa2Se4 crystals. HgGa2Se4 single-crystals are direct-band semiconductors as ZnAl2Se4. The HgGa2Se4 compound crystallizes in tetrahedral lattice with S42 space group. The band structure of these crystals is split taking into account a pseudopotential configuration of Hg (5d106s2), Ga (3d104s24p1) and Se (3d104s24p4) atoms [2].  The HgGa2Se4 crystals were grown by gas-transport method in ampoules and were plates with mirrored surfaces ~ 5x7 mm and 2 - 6 mm thickness. The plate‘s surfaces were parallel with c axis and could be recognized visually. Low-temperature spectra of crystals deposed in closed helium LTS-22 C 330 optical cryogenic system were measured on MDR-2 spectrometer with optical efficiency 1:2 and linear dispersion 7 Ǻ/mm. The measurements of resonance Raman scattering and photoluminescence were carried out by help of spectrometer DFS-32 with optical efficiency 1:5 and linear dispersion 5 Ǻ/mm.  The ground and excited states of excitonic series A, B, C and D were discovered in HgGa2Se4 crystals in Brillouin zone center in the region of band gap. The Γ4 excitons (A series) and the Γ5 excitons (B and C series) are allowed in E||c and in Ec polarizations, respectively. The Γ4 symmetry excitons are formed by electrons of conduction band C1 of Γ6 symmetry and holes of valence band V1 of Γ7 symmetry. The effective mass of electrons mc is equal to 0.26m0 and holes masses mv1, mv2 and mv3 are equal to 2.48m0, 2.68m0 and 1.06m0, respectively in Γ point of Brillouin zone. The splitting of valence bands in Brillouin zone center by crystal field (Δcf = 70 meV) and spin-orbital interaction (Δso = 250 meV) were estimated.  When excited by the 5145Å Ar+ laser line of HgGa2Se4 crystals at 10 K, emission lines shifted to the long-wave side from the exciting line to an energy equal to one, two, three, etc. LO are phonons are observed. The lines are due to resonant Raman scattering which are superimposed on the luminescence spectra from the ground states of excitons. For lines located near the exciton resonance, an increase in intensity is observed.  Direct transitions revealed in reflection (R) and wavelength modulated reflection (ΔR/Δλ) spectra were discussed and identified in all actual points of Brillouin zone in framework of recent theoretical calculations of band structure of HgGa2Se4 crystals. The optical constants (n, ε1 and ε2) for E||c and Ec polarizations in energy interval 2 - 6 eV were calculated from measured reflection spectra by Kramers-Kronig relations.