In this thesis, we represent Classical Hall Effect and Quantum Hall Effectrnstudies at high magnetic field and low temperature in 2DEG and in highrnquality and charge carrier bilayer graphene samples for the degeneraternLandau levels, with a particular emphasis on Integer and FractionalrnQuantum Hall effects. And also we have studied about the equation ofrnquantization energy (Landau levels) by using Landau gauge and symmetricrngauge solutions in 2DEG and bilayer graphene samples.rnIn 2DEG and in bilayer graphene, the thermal energy is less thanrnquantization energy (