We measure the far-infrared magneto-optical Kerr rotation and reflectivity spectra of graphite and achieve a highly accurate unified microscopic description of all data in abroad range of magnetic fields by taking rigorously the c-axis band dispersion and the trigonal warping in to account. We find that the second- and the forth-order cyclotron harmonics are optically almost as strong as the fundamental resonance even at high fields. They must play, therefore, a major role in magneto-optical and magneto- plasmonic applications based on Bernal stacked graphite and multilayer graphene.