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In this book we have systematically investigated and represented the structural, electronic, phase transition, thermal properties of the heaviest lanthanide compounds (LuX, X = N, P, As) viz. lutetium nitride (LuN), lutetium phosphide (LuP) and lutetium arsenide (LuAs) using an ab-initio calculations based on the density functional theory (DFT). In the subsequent section crystal structure, symmetry and space group have been discussed which are related to Lutetium Monopnictides. It is followed by a brief discussion of rare-earth ions. Survey of the literature on the theoretical and experimental work already available on related compounds are done. The relative stabilities of LuX at high pressures in the NaCl (B1), CsCl (B2), zinc blende (B3), and body-centered tetragonal (BCT) structures are analyzed. Lu-monopnictides show a structural transition from B1 to B2 and BCT phase under compression. The computed values of a, B0, B0', E0 and PT are obtained for Lu-compounds are tabulated. Thermal properties such as Gruneisen parameter, thermal expansion coefficient, bulk modulus, specific heat, and entropy have been studied at high temperature and high pressure.