The graphite crystal represents a stack of rigid graphene monolayers bound by Van der Waals forces. The shear phonon mode corresponds to the neighboring layers oscillating in the opposite directions. Phonons are typically probed by Raman spectroscopy, and the observed spectrum of the shear phonon mode has a peculiar Fano shape which arises due to quantum interference when a discrete mode is coupled to a continuum of excitations. In the case of graphite, the continuum was suggested to originate from electronic excitations. A recent experiment has shown that the shape of the shear phonon peak strongly changes with the magnetic field. The preliminary explanation of this result is that the magnetic field quantizes the electronic bands of graphite into Landau levels, so the structure of the electronic excitation continuum is modified. To put this explanation on a firm ground, we have to construct a quantitative theory of this effect. The goal of the internship is to calculate the coupling of the shear mode phonons to the electronic excitations in a magnetic field using the tight-binding model of Slonczewski, Weiss, and McClure. When the coupling is found, we can proceed to the calculation of the Raman spectrum.