One dimensional quantum Ising model with nearest neighbor interaction in transverse magnetic field is one of the simplest spin models shows quantum phase transition. This model has been solved with different methods exactly. In this thesis, at first, we solve this model in different kind of magnetic field and with new method called Continuous Unitary Transformations (CUT) or Flow equations. We show that these models posses a quantum critical point and they are in the same universality class. Then we apply CUT method on one dimensional quantum Ising model with next nearest neighbor interaction to study its physical properties. We show that CUT is not a good method for solving this kind of many-body problems.