Higgs Physics at the Muon Collider

A multi-TeV muon collider produces a significant amount of Higgs bosons allowing for precise measurements of its couplings to Standard Model fundamental particles. Moreover, Higgs boson pairs are produced with a relevant cross-section, allowing for the determination of the second term of the Higgs potential by measuring the double Higgs production cross-section and therefore the trilinear self-coupling term. This contribution aims to give an overview of the Higgs measurement accuracies expected for the initial stage of the muon collider at s=3TeV with an integrated luminosity of 1ab-1 and for the target center-of-mass energy at 10TeV with 10ab-1 integrated luminosity. The results are obtained using the full detector simulations which include both physical and machine backgrounds.