Abstarct: The magnetic monopole is particle similar to electron except that its electric charge is much larger than that of electron. In 1931, Dirac proposed the existence of particles, which intrinsically produced magnetic fields. The discussions regarding the magnetic monopole, however, were also released before Dirac. Namely, Poincare, in 1896, analyzed the motion of an electric charge in the field of long narrow magnetic coil which produced at one end a field similar to that of magnetic monopole. The lack of symmetry between electric and magnetic charges is one of the oldest puzzles in physics. In the beginning of the 19th century, some arguments were released regarding the possible relation of magnetic of material and existence of magnetic monopole. The idea of magnetic monopole in Dirac’s mind was concurrent with his proposition regarding the existence of particles similar to electron with positive charge which he called positron. In this thesis, we first briefly review some concepts regarding the properties of magnetic monopole and the possible observation of magnetic monopole in an artificial magnetic field. We next explain the Maxwell equation and the magnetic monopole potential in chapter 2. In section 3, we have analyzed the Micz-Kepeler system and Kaluza-Klein system in the presence of magnetic monopole. In section 4, we consider the approximate analytical solution of the Klein-Gordon potential for the Hulthen potential in the presence of Aharanov-Bohm magnetic field and report the energy spectrum and the wavefunctions of the system. In section 5, we work on the Dirac magnetic monopole field with the Coulomb and Aharanov-Bohm field, solve the problem in three spatial dimensions and describe the dependence of the energy eigenvalues on the engaged potential parameters and other constants of the problem. Finally, in section 6, we consider the (3+1)-dimensional Dirac equation with nonminimal coupling of radial linear isotropic electromagnetic field and calculate the thermodynamic properties of the system.