This book contains some problems associated with the linear and nonlinear propagations of dust-ion-acoustic (DIA) waves in a collisionless four-component unmagnetized dusty plasma system (nonextensive electrons, inertial negative ions, Maxwellian positive ions, and negatively charged static dust grains). The normal mode analysis is used to examine the linear properties and the reductive perturbation method is used to derive the nonlinear equations, namely, the Burgers, the modified Burgers (mB), the higher order Burgers (HOB), the Korteweg-de Vries (K-dV), the modified K-dV (mK-dV), and the Gardner equations. Their solitary wave (in case of K-dV, mK-dV, and Gardner equations) and shock wave (in case of Burgers and mB equations) solutions are obtained, and analyzed numerically. The findings of our results obtained from this book may be useful in understanding the linear and nonlinear structures and the characteristics of DIA waves propagating in both space and laboratory dusty plasmas.