The optical properties of HgSe grown by molecular-beam epitaxy have been studied over a wide range of frequencies covering the ${\mathit{E}}_{0}$, ${\mathit{E}}_{1}$, and ${\mathit{E}}_{1}$+${\mathrm{\ensuremath{\Delta}}}_{1}$ gaps. Theoretical calculations of the dielectric function are used in deriving fundamental material parameters for HgSe. The refractive index has thus been determined at room temperature up to 1 eV. A comparision of temperature-dependent measurements of the fundamental absorption in HgSe with theoretical calculations using various sets of band structure parameters has yielded an estimate of the temperature shift of the ${\mathit{E}}_{0}$ gap. The carrier concentration as derived from van der Pauw measurements was shown to be inconsistent with optical determinations of the Fermi energy. Differences in the absolute values of the absorption coefficient compared to theoretical spectra have been observed and compared to data reported for bulk HgSe. The critical point energies ${\mathit{E}}_{1}$ and ${\mathit{E}}_{1}$+${\mathrm{\ensuremath{\Delta}}}_{1}$ could be determined in the temperature range 5\char21{}300 K by fitting reflection measurements to theoretical spectra derived from the dielectric function.