In this thesis, primarily we reviewed first and second quantization representations in order to be used for calculation of energy bands, then we mentioned several simple examples of these kind of calculations. Next, we briefly explained the concept of topology and its application in physics and reviewed a short history of topological matter. We pointed out some symmetries that play a role in topological phases of matter and we introduced a classification of nodal-line semi-metals with respect to symmetries. At the end we specifically scrutinized Co 2 MnGa as a candidate for Hopf-link and nodal-chain topological semi-metal. We calculated energy bands of this crystal in second quantization representation and showed that its energy bands undergo specific properties corresponding to nodal-chain and Hopf-link topological semi-metals.
