The comparison between the measurement and the Standard Model prediction of the anomalous magnetic moment of the muon (aμ) is a way to search for physics beyond the Standard Model. Recently, the Fermilab Muon g−2 experiment measured aμ with a precision of 200 parts per billion (ppb), while the theoretical prediction of aμ is limited by the uncertainty in the leading-order hadronic vacuum-polarization contribution (aμHLO) as the two calculation methods, namely the dispersive approach and the lattice QCD, yield different results. The MUonE experiment proposes an alternative and independent way to precisely measure aμHLO through a unique direct measurement, which can be used to cross-check the theoretical value.