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The optical conductivity of graphite in quantizing magnetic fields isstudied. Both the dynamical conductivities, longitudinal as well as Hall's, areanalytically evaluated. The conductivity peaks are explained in terms ofelectron transitions. We have shown that the trigonal warping in graphite canbe considered within the perturbation theory at the strong magnetic fieldlarger than 1 T approximately. The main optical transitions obey the selectionrule with $\Delta n=1$ for the Landau number $n$, however the $\Delta n=2$transitions due to the trigonal warping with the small probability are alsoessential. The Kerr rotation and reflectivity in graphite in the quantizingmagnetic fields are calculated. Parameters of the Slonczewski--Weiss--McCluremodel are used in the fit taking into account the previous dHvA measurementsand correcting some of them for the case of the strong magnetic fields.

Quantum magneto-optics of graphite with trigonal warping