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Precision measurements in weak decays of heavy flavored hadrons can test in unique ways our understanding of the fundamental interactions and of the observed baryon asymmetry in the Universe. The high sensitivity of such decays to beyond-Standard-Model physics, combined with the lack of major discoveries in direct production of new particles, motivates the continuation of a strong heavy-flavor program in the next decades. The observation of several anomalies by the BaBar, Belle and LHCb experiments in such decays, including evidence for violation of lepton universality, provides particular motivation to vigorously pursue this program. While the mass scales probed by direct searches for non-Standard-Model phenomena at the energy frontier will only marginally increase in the near future, a substantial advancement is expected in the study of weak decays of $b$ and $c$ quarks. The next 10 to 20 years will see the development of a highly synergistic program of experiments at both $pp$ and $e^+e^-$ colliders. This program will be complemented by advancements in theory, including both lattice and continuum calculations. Experimental measurements and theory predictions of several key observables will reach unprecedented precision and will allow to test the Standard Model in ways that have not been possible thus far. With a strong participation in this program, the US high-energy-physics community will remain at the forefront of indirect searches for new physics and retain its leading role in expanding humankind's understanding of fundamental interactions.