The measurements of the inclusive and differential fiducial cross sections of the Higgs boson decaying to a pair of photons are presented. The analysis is performed using proton-proton collisions data recorded with the CMS detector at the LHC at a centre-of-mass energy of 13TeV and corresponding to an integrated luminosity of 137 fb^-1. The inclusive fiducial cross section is measured to be sigma(fid) = 73.4^+5.4_-5.3(stat)^+2.4_-2.2(syst) fb, in agreement with the standard model expectation of 75.4 +/- 4.1 fb. The measurements are also performed in fiducial regions targeting different production modes and as function of several observables describing the diphoton system, the number of additional jets present in the event, and other kinematic observables. Two double differential measurements are performed. No significant deviations from the standard model expectations are observed.