In this dissertation, we study the effects of the electron-electron Coulomb interaction in graphene. We first analyze the sublattice symmetric (i.e. density-density) and antisymmetric response functions and show that the latter has a singularity as a function of the coupling constant (which can be changed by changing the background dielectric constant) signalling the transition to the insulating phase. Furthermore, even for coupling constant smaller than the critical value, the effect of the Coulomb interaction is manifested in that the antisymmetric response function has a power law dependence on the momentum transfer and the exponent is a continuously varying function of the coupling constant. We also calculate the symmetric response for a model Hamiltonian numerically. The effects of the Coulomb interaction is also manifested as a correction to the excitation energy from a filled Landau level. We analyze the eigenvalue problem for magnetoexcitons in detail and compare the theory with experiments. Finally, we study how stable the high field quantum Hall states are against Landau level mixing, which is also an interaction effect, as the magnetic field is decreased.