High-energy phenomena in the cosmos, and in particular processes leading to the emission of gamma- rays in the energy range 10 MeV - 100 GeV, play a very special role in the understanding of our Universe. This energy range is indeed associated with non-thermal phenomena and challenging particle acceleration processes. The technology involved in detecting gamma-rays is challenging and drives our ability to develop improved instruments for a large variety of applications. GAMMA-LIGHT is a Small Mission which aims at an unprecedented advance of our knowledge in many sectors of astrophysical and Earth studies research. The Mission will open a new observational window in the low-energy gamma-ray range 10-50 MeV, and is configured to make substantial advances compared with the previous and current gamma-ray experiments (AGILE and Fermi). The improvement is based on an exquisite angular resolution achieved by GAMMA-LIGHT using state-of-the-art Silicon technology with innovative data acquisition. GAMMA-LIGHT will address all astrophysics issues left open by the current generation of instruments. In particular, the breakthrough angular resolution in the energy range 100 MeV - 1 GeV is crucial to resolve patchy and complex features of diffuse sources in the Galaxy as well as increasing the point source sensitivity. This proposal addresses scientific topics of great interest to the community, with particular emphasis on multifrequency correlation studies involving radio, optical, IR, X-ray, soft gamma-ray and TeV emission. At the end of this decade several new observatories will be operational including LOFAR, SKA, ALMA, HAWK, CTA. GAMMA-LIGHT will fill the vacuum in the 10 MeV-10 GeV band, and will provide invaluable data for the understanding of cosmic and terrestrial high-energy sources.