In this thesis, we consider a superlattice composed of normal and topological insulators and analyze the superconducting states that can form in this composite system. To consider the electron pairing, we include both the Coulomb interaction and the electron-phonon interaction between interface states in the superlattice. The Coulomb potential energy is obtained by solving the Green’s function for the superlattice approximately, while the electron-phonon interaction is included by considering the acoustic phonons. A mean field theory is constructed by considering interactions between nearest-neighbouring interfaces. We obtain the gap equations and discuss the phase diagram for different interaction strengths at different regimes of thickness. It is shown that at certain interaction strength, the triplet pairing dominates and the system is a topological superconductor.