Physics at the FCC-ee

The physics program accessible in $e^+e^-$ collisions at the Future Circular Collider (FCC-ee) is summarized. The FCC-ee aims at collecting multi-ab$^{-1}$ integrated luminosities in $e^+e^-$ at $\sqrt{s}$ = 90, 160, 240, and 350 GeV, yielding 10$^{12}$ Z bosons, 10$^{8}$ W$^+$W$^-$ pairs, 10$^{6}$ Higgs bosons and $4\cdot 10^{5}$ top-quark pairs per year. Such huge data samples combined with a $\cal{O}(100 \rm keV)$ c.m. energy uncertainty will allow for Standard Model measurements with unparalleled precision and searches for new physics in regions not probed so far. The FCC-ee will be able to (i) indirectly discover new particles coupling to the Higgs and electroweak bosons up to scales $\Lambda \approx$ 7 and 100 TeV; (ii) perform competitive SUSY tests at the loop level in regions beyond the LHC reach; and (iii) achieve the best potential in direct collider searches for dark matter and sterile neutrinos with masses below 60 GeV.