Two facility concepts have been considered as potential pathways to the future of particle physics at the energy frontier in Europe: FCC-hh, a 100 TeV circular hadron collider and CLIC, a 3 TeV linear lepton (i.e. electron-positron) collider. The recent European Accelerator R&D Roadmap includes a novel option, a 10 or more TeV muon collider, which expands the lepton collider energy reach and promises compact dimensions, high efficiency and limited cost. Muons are point-like particles, in contrast to hadrons; a 10 TeV muon collider would have a comparable physics case, for a number of physics processes, to a 100 TeV hadron collider. The muon collider promises high benefit but also faces a significant risk, as it is the first of its kind and uses novel advanced technologies. The MuCol design study will address the core challenges identified in the Roadmap, develop the concept and technologies and demonstrate: • the physics case of the muon collider is sound and detector systems can yield sufficient resolution and rejection of backgrounds; • no principle technological issues will prevent the achievement of a satisfactory performance of the accelerator or the detectors; • the muon collider provides a highly sustainable energy frontier facility compared to other equivalent colliders; and • exploiting synergies with other scientific and industrial R&D projects, can provide Europe a leading edge in discovery potential and development of associated technologies. The final report will include a thorough assessment of benefits and risks of the accelerator and detector complex, including an evaluation of the scientific, industrial and societal return beyond high-energy physics, the cost scale and sustainability of the complex and the impact arising from an implementation on the CERN site. This will allow the next European Strategy for Particle Physics Update (ESPPU) process to make informed choices for the selection of the next large collider to be built in Europe.