Short summary: Density Functional Theory (DFT) is one of the most widely used tools in computational materials science, yet its foundations and practical workings remain unfamiliar to many that don’t employ it one a day-to-day basis. The seminar provided an accessible introduction to DFT, tracing the conceptual path from the Schrödinger equation to the Hohenberg-Kohn theorems and the Kohn-Sham formalism, and discussing the key practical choices involved in a DFT calculation – pseudopotentials, basis sets, and exchange-correlation functionals. The second part illustrated the capabilities of these methods through two case studies. The first focused on the high-pressure phase behaviour of SrGeO3, where DFT calculations of enthalpies as a function of pressure successfully confirmed experimentally observed phase transitions and rationalised the onset of amorphization. The second introduced evolutionary crystal structure prediction using the USPEX algorithm, applied to the yttrium-nitrogen system under pressure. By combining structural searches with electronic structure analysis – including density of states calculations – it was possible to identify stable Y-N phases, map their pressure-dependent stability, and resolve the nature of the nitrogen-nitrogen bonding in the predicted structures.