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Recently the analysis of nature and characteristic of the nonlinear electrostatic waves of dusty plasmas has drawn a sharp attention to the Researchers of Computational Plasma Science. In this book, the properties of planar and nonplanar dust-ion-acoustic (DIA) solitons, shocks and double layers are discussed both analytically and graphically. The higher order nonlinear equation 'Gardner Approach' is introduced here to analyze the solitons beyond the critical limit of K-dV approach. Besides, planar and nonplanar Burgers equations are also discussed. It is observed that the multi-species plasma model or Bi-Maxwellian-electron plasma model play an important role to modify the basic features (polarity, amplitude, width, etc.) of the DIA waves. This book introduces a new horizon for the two-electron-temperature dusty plasma model along with its rigorous analysis of DIA waves. The implications of the obtained results in understanding the nonlinear electrostatic perturbation observed in double plasma machines, rf discharges, noctilucent clouds, earth atmosphere, etc. where the two population of thermal electron can dominate the wave dynamics, are also discussed in this book.