The Galactic Explorer with a Coded Aperture Mask Compton Telescope (GECCO) is a novel Explorer-class concept for a next-generation telescope covering the poorly explored hard X-ray and soft gamma-ray energy regimes. The instrument is based on a novel CdZnTe imaging calorimeter and a deployable coded aperture mask, which enable it to reach 1 arcmin angular resolution and 1\% energy resolution. GECCO will connect the arcminute angular resolution observations from X-ray telescopes to high-energy images of the Galactic plane provided by Fermi-LAT, and will focus on the exploration of heavily populated sky regions such as the Galactic Center and the Carina and Cygnus regions to decipher the nature of their emission. These measurements will probe with unprecedented capabilities the possible origin of this emission as dark matter, new types of sources, or currently unresolved populations of point sources. Uncoded observations with GECCO’s Compton telescope will provide wide field-of-view sky monitoring for transient events, synergizing with gravitational wave and high-energy neutrino facilities. In addition, GECCO will conduct a high-sensitivity search for the positron sources in the Galactic Center responsible for the enigmatic 511 keV positron annihilation line excess, will search for as-yet untested candidates for dark matter, will detect and identify high-redshift blazars with excellent angular resolution, and will explore Galactic chemical evolution and sites of explosive element synthesis.