  The sky at MeV energies is currently poorly explored. Here we present an
innovative mission concept that builds on and improves past and currently
proposed missions at such energies. We outline the motivations for combining a
coded mask and a Compton telescope and we define the scientific goals of such a
mission. The Galactic Explorer with a Coded Aperture Mask Compton Telescope
(GECCO) is a novel concept for a next-generation telescope covering hard X-ray
and soft gamma-ray energies. The potential and importance of this approach that
bridges the observational gap in the MeV energy range are presented. With the
unprecedented angular resolution of the coded mask telescope combined with the
sensitive Compton telescope, a mission such as GECCO can disentangle the
discrete sources from the truly diffuse emission. Individual Galactic and
extragalactic sources are detected. This also allows to understand the
gamma-ray Galactic center excess and the Fermi Bubbles, and to trace the
low-energy cosmic rays, and their propagation in the Galaxy. Nuclear and
annihilation lines are spatially and spectrally resolved from the continuum
emission and from sources, addressing the role of low-energy cosmic rays in
star formation and galaxy evolution, the origin of the 511 keV positron line,
fundamental physics, and the chemical enrichment in the Galaxy. Such an
instrument also detects explosive transient gamma-ray sources, which enable
identifying and studying the astrophysical objects that produce gravitational
waves and neutrinos in a multi-messenger context. By looking at a poorly
explored energy band it also allows discoveries of new astrophysical phenomena.
