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Homotopy Perturbation Elzaki Transform Method is a best tool for finding the solution of nonlinear partial differential equation. The theoretical study of HPETM and its applications to nonlinear differential equation is an important part of this book. The main objective of the book is to discuss HPETM theoretically and applied it in ground water flow problems and nonlinear diffusion equation with different special cases to study the behavior of solutions.