Astrophysical observations at (sub-)mm wavelengths (λ from ~300 μm to ~3mm) allow us to study the cold and dense material in the Universe, hence probing the formation of stars and planets, and the interstellar and circumgalactic medium of galaxies across all cosmic times. The current generation of 10-m class single dish telescopes delivered the first surveys of the sky at (sub- )mm wavelengths, allowing us to go far beyond the previously optical/IR- biased view of the Universe. Follow- up observations with interferometers then revealed, in exquisite detail, the morphology and kinematics of such (sub-)mm sources, enabling tests and revisions of theoretical models for the formation and evolution of planets, stars, and galaxies. However, it is now clear that without a step change in the capabilities of single-dish facilities in the 2030s, interferometers (like the ALMA observatory) will soon become source-starved. The current generation of 10- m class single dish telescopes, with their limited field of view, spatial resolution, and sensitivity, can only reveal the ‘tip of the iceberg’ of the (sub-)mm source population, both for Galactic and extragalactic studies. These limitations cannot be compensated for by interferometers, which are all intrinsically affected by a low mapping speed and by the loss of diffuse extended signals. The Atacama Large Aperture Submillimeter telescope (AtLAST) project is a concept for a 50m -diameter single dish observatory to be built near the ALMA site. With its extremely large field of view (the goal is ~ 2 degrees), spatial resolution (up to ~1.5” at 350 μm), and sensitivity to both point sources and large-scale structures, AtLAST will be transformational for all fields of Astronomy in the 2030s. Here we will describe the recently approved Horizon2020 project to deliver a comprehensive design study for such a next-generation single-single dish facility.