This book is written in a lucid and systematic way for advanced postgraduates and researchers studying applied mathematics, plasma physics, nonlinear differential equations, nonlinear optics, and other engineering branches where nonlinear wave phenomena is essential. In sequential order of the book's development, readers will understand basic plasmas with elementary definitions of magnetized and unmagnetized plasmas, plasma modeling, dusty plasma and quantum plasma. Following which, the book describes linear and nonlinear waves, solitons, shocks and other wave phenomena, while solutions to common nonlinear wave equations are derived via standard techniques. Readers are introduced to elementary perturbation and non-perturbation methods. They will discover several evolution equations in different plasma situations as well as the properties of solitons in those environments. Pertaining to those equations, readers will learn about their higher order corrections, as well as their different forms and solutions in non-planar geometry. The book offers further studies on different types of collisions between solitons in plasma environment, phenomena of soliton turbulence as a consequence of multi-soliton interactions, properties of large amplitude solitary waves which are discovered via non-perturbative Sagdeev's Pseudopotential Approach, as well as the speed and shape of solitons. Finally, the book reveals possible future developments of research in this rich field.