Magnetic topological insulator (TI) has been theoretically proposed to be a platform for inducing magnetic monopole and exhibit fascinating quantum phenomena, whereas topological superconductor can host Majorana fermions, particles that are their own antiparticles, which can be manipulated for topological quantum computing. In this dissertation, we experimentally demonstrated that by intercalation of different transition metals in the van der Waals gaps of Bi2Se3 TI, magnetism and even superconductivity can be induced. In FexBi2Se3, antiferromagnetism is induced with a transition temperature at ~ 100 K. Coexistence of the Dirac surface state with magnetism in antiferromagnetic TI that has been predicted by the theoretical study is verified. We also found the Dirac fermions originate from the bulk acting as many parallel 2D conduction channels on the material. In MnxBi2Se3 , paramagnetism is induced. From Shubnikov-de Haas oscillations and quantum Hall effect (QHE) observation, we found the existence of Dirac fermions originate from the bulk, which is similar to the case of Fex Bi2Se3. Due to the origin of the QHE in FexBi2Se3 and MnxBi2Se3 systems is from the bulk acting as many 2D conduction channels, the electric field exfoliation method is invented. This method is capable of obtaining a clean sample from different layered crystalline materials with the thicknesses in the range of nm and expecting to observe QHE from surface state on both materials. Superconductivity is also induced in NbxBi 2Se3 with a critical temperature of Tc = 3.2 K while the Dirac surface dispersion in its normal state is still preserved. The onset of hysteretic magnetization in NbxBi 2Se3 below Tc suggests spontaneous time-reversal symmetry breaking in the superconducting state. Superconducting and magnetism mutually assist each other to give rise to a symbiosis state of this two phases.