Traditionally, quantum phases in physics have been studied on the basis of local order parameters and the concept of spontaneously symmetry breaking. However, recently it has been recognized that there are phases which cannot be captured by local order parameters. In these new phases, topology of wave functions plays important roles to characterize their properties. In this talk, I would like to explain materials supporting non-trivial topology in the ground states. These materials show universal physical properties such bulk-boundary correspondence, as well as exotic excitations like Majorana fermions in condensed matter physics. I also would like to explain how to classify such topological materials.