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It is a book based on first principles calculations of various crytal properties of some Rare earth compounds along with III-V semicondutors. The electronic, mechanical, structural and magnetic properties of these compounds have been studied at ambient as well as at high pressures. The present theoretical results are in good agreement with the experimental data and better than those obtained by other earlier workers by different methods. Few of the materials show semi-metallic while some others are showing semiconducting nature. These Rare earth materials show polymorphic phase transformation from B1 to B2, B3 to B1 phase. Some Rare earth also show iso-structural electronic transformation before polymorphic transformation. The Rare earth compounds are found to be magnetic at ambient pressures.