  The optical conductivity of graphene, bilayer graphene, and graphite in
quantizing magnetic fields is studied. Both dynamical conductivities,
longitudinal and Hall's, are analytically evaluated. The conductivity peaks are
explained in terms of electron transitions. We have shown that trigonal warping
can be considered within the perturbation theory for strong magnetic fields
larger than 1 T and in the semiclassical approach for weak fields when the
Fermi energy is much larger than the cyclotron frequency. The main optical
transitions obey the selection rule with \Deltan = 1 for the Landau number n,
however the \Deltan = 2 transitions due to the trigonal warping are also
possible. The Faraday/Kerr rotation and light transmission/reflection in the
quantizing magnetic fields are calculated. Parameters of the
Slonczewski-Weiss-McClure model are used in the fit taking into account the
previous dHvA measurements and correcting some of them for the case of strong
magnetic fields.
