We present concept of a new multi-satellite Universat-SOCRAT project aimed to study transient phenomena in the upper atmosphere such as transient luminous events (TLEs) and terrestrial gamma-ray flashes (TGFs). It is a new space project of Lomonosov Moscow State University based on the use of a few satellites in the near-Earth orbit for real-time monitoring of radiation environment, natural (asteroids, meteoroids) and artificial (space debris) potentially dangerous objects, electromagnetic transients including cosmic gamma-ray bursts, terrestrial gamma-ray flashes, and optical and ultraviolet bursts in the Earth's atmosphere. Study of TLEs and TGFs remains an important and demanding task despite of a multitude of recently acquired data for these phenomena. This might be explained by the absence of comprehensive theoretical understanding of physical nature of high-energy processes in the Earth's atmosphere. Multi-wavelength synchronous observations with moderate accuracy of localization of TGF and TLE events are necessary to gain an insight of physics governing these high-energy processes in the Earth's atmosphere. In the article, we present results of TLE observations in space experiments of Moscow State University and discuss advanced instruments for optical observations of TLEs, as well as gamma-ray burst monitor and tracking gamma spectrometer for TGFs observations.