This work was originally written as an M. Sc thesis in 2011. In this work, a rigorous theoretical investigation has been made on dust-ion-acoustic (DIA) linear and nonlinear waves in planar and nonplanar dusty plasma systems. The three popular approaches: the Korteweg-de Vries (K-dV), the modified Korteweg-de Vries (mK-dV), and the Garder which are used to analyze planer and non-planer dusty plasma systems are derived and discussed in details. The characteristic ranges, applications and comparisons between these three approaches are explained and discussed in brief. This books also contains the exact analytical solution of Garder Soliton and Double layers which has been used in more than 100 of research articles after it was first published in 2011 as a paper by the author. The applications of the approaches and plasma studies in laboratories and astrophysics are also pinpointed in the book.