This book deals with the ab-initio pseudo- and full-potential based computation of the electronic, mechanical, elastic, thermo-physical study of transition metal carbides (TiC, ZrC, HfC, VC, NbC and TaC) and nitrides (TiN, ZrN, HfN, VN, NbN and TaN) at ambient and high pressure conditions . Phase transition properties have also been computed. Valence charge density of these materials have been calculated in (100) plane in their parent NaCl structure and in (110) plane in their high pressure CsCl structure along with their band structures and density of states to better understand their chemical bonding.