In this paper we demonstrate how twilight sky brightness measurements can be used to obtain information about stratospheric aerosols. Beside this, the measurements of the distribution and the variability of the twilight sky brightness may help to understand how the stratospheric aerosols affect the radiation field, which is important for correct calculations of photodissociation rates. Multispectral measurements of twilight sky brightness were carried out in Abastumani Observatory (41.8°N, 42.8°E), Georgia, South Caucasus, during the period (1991-1993) when the level of stratospheric aerosols was substantially enhanced after the 1991 Mount Pinatubo eruption. The twilight sky brightness was measured at 9 wavelengths (422, 474, 496, 542, 610, 642, 678, 713, and 820 nm) for solar zenith angles from 89° to 107°. There are clear indications of a growth of the stratospheric aerosol layer after the eruption of Mount Pinatubo that manifests itself by "humps" in twilight sky brightness dependences versus solar zenith angle. Similar features were obtained using a radiative transfer code constrained by the SAGE II aerosol optical thicknesses. It is shown how an enhancement of stratospheric aerosol loading perturbs the twilight sky brightness due to light scattering and absorption in the aerosol layer. The influence of ozone variations and background stratospheric aerosols on twilight sky brightness has also been analyzed. The optical thicknesses of the stratospheric aerosol layer obtained from the twilight measurements of 1990-1993 show a good agreement with SAGE II results. The spectral variations of the stratospheric aerosol extinction for pre-Pinatubo and post-Pinatubo measurements reflect the aerosol growth after the eruption. Finally, the utilization of twilight sky brightness measurements for validation of satellite-based measurements of the stratospheric aerosol is proposed.