Recently the analysis of nature and characteristic of the nonlinear electrostatic waves of dusty plasmas has grown a deep attention to the Researches of Computational Plasma Science. In this book, a rigorous theoretical investigation has been made on linear and nonlinear propagation of dust-ion-acoustic (DIA) waves in a dusty plasma with nonthermal distribution of plasma particles. The linear dispersion relation of the DIA waves, which exist in such an unmagnetized dusty plasma system has been discussed both analytically and graphically in this book. Then the work has been generalized to a magnetized dusty electronegative plasma in order to study obliquely propagating DIA solitary waves, and their multi-dimensional instabilities. The combined effects of the external magnetic field and nonthermal distribution of negative electron, which are found to significantly modify the basic properties of small but finite-amplitude DIA solitary waves, are rigorously examined in this book. The basic features (viz.amplitude, width, stability etc) and the underlying physics of the DIA solitary waves, which are relevant to space and laboratory dusty plasmas, are also briefly discussed in this book.