The CrI3 is a multilayered compound, where the magnetic Cr ions form a honeycomb lattice. The strong anisotropies of the Kitaev type make CrI3 interesting for both experiments and theory. The M.Sc. project aims to develop an advanced mean-field theory to describe the magnetic field phase diagram of this compound and a multiboson spin-wave theory to describe the ESR spectra. This work will be done in close collaboration with the experimental group of Ferenc Simon. The project will include analytical calculations supported by light numerics.