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In the last decades there has been a growing interest in the field of Dusty Plasma. The presence of static charged dust in plasma can modify the standard plasma modes. Recent experiments have shown that under appropriate conditions dust grains crystallize. This is significant because it provides an easily observable model for studying the dynamics and structure of crystal lattice, solid liquid phase transitions. This book has been planned to deals with a detail investigation of low frequency dissipative drift instability in dusty plasma. Besides that, Coulomb crystal formation in strongly coupled dusty plasma has been elaborately discussed both in presence and absence of magnetic field using molecular dynamics (MD) simulation. The author has discussed the critical magnetic field for phase transition from crystalline to liquid state of strongly coupled magnetized plasma. The text is enriched with MD simulational results which may find application in various space and laboratory plasma situations.