Partial differential equations and an extensive application in physical, biological and engineering systems. Most of the natural phenomena are based on the partial differential equations like vibrations of solids, diffusion of chemicals, heat transfer, electromagnetic waves, etc. This book provides an introduction to partial differential equations (PDEs) and to the techniques that have proved useful in analyzing them. Our purpose is to make students familiar with the basic concepts related to the subject, and to teach an effective knowledge of the most important techniques of analysis of the solutions of the equations. The book comprises of four chapters. The first chapter deal with the general introduction about the Partial differential equations and classiffcation of first order PDEs with appropriate examples for better understanding. The second chapter is related with the second order PDEs and general solution of higher order PDE with constant coefficients. The third chapter is devoted to three basic PDEs-Heat equation, Wave equation and Laplace equation, and different techniques used to and out the solution of these equation. In the last chapter, basic introduction related to the Fourier transformation has been incorporated so as to make student familiar with the most and beautiful concept and some basic theorems.