In this white paper for the 2021 Snowmass process, we give a description of the proposed Future Circular Collider (FCC) project and its physics program. The paper summarizes and updates the discussion submitted to the European Strategy on Particle Physics. After construction of an ≈ 90 km tunnel, an electronpositron collider based on established technologies allows world-record instantaneous luminosities at center-of-mass energies from the Z resonance through the ZH and WW and up to tt thresholds, enabling a very rich set of fundamental measurements including Higgs couplings determinations at the subpercent level, precision tests of the weak and strong forces, and searches for new particles, including dark matter, both directly and via virtual corrections or mixing. Among other possibilities, the FCC-ee will be able to (i) indirectly discover new particles coupling to the Higgs and/or electroweak bosons up to scales Λ ≈ 7 and 50 TeV, respectively; (ii) perform competitive SUSY tests at the loop level in regions not accessible at the LHC; (iii) study heavy-flavor and tau physics in ultra-rare decays beyond the LHC reach, and (iv) achieve the best potential in direct collider searches for dark matter, sterile neutrinos, and axion-like particles with masses up to ≈ 90 GeV. The tunnel can then be reused for a proton-proton collider, establishing record center-of-mass collision energy, allowing unprecedented reach for direct searches for new particles up to the ≈ 50 TeV scale, and a diverse program of measurements of the Standard Model and Higgs boson, including a precision measurement of the Higgs self-coupling, and conclusively testing weakly-interacting massive particle scenarios of thermal relic dark matter. The FCC-ee and FCC-hh physics and accelerator programs are remarkably synergistic and complementary. The program builds on the stable funding provided by the CERN member states and the existing, long-standing worldwide partnerships built via the LHC, but requires substantial contributions both intellectual and financial from the US and other non-CERN-members to become a reality. 8.3.3 Decays of the tau to three muons and to a muon and a photon . . .