This course addresses basics definitions and concepts of partial differential equations and its applications. So, it covers techniques of solutions of linear and quasi-linear first order PDE by eliminating arbitrary constants or arbitrary functions, Lagrange method and techniques of solutions of fully nonlinear first order PDEs. Also, it covers linear partial differential equations of higher order, which include elliptic, parabolic, and hyperbolic PDE, reduction to canonical form and general solutions, introduction to Fourier series, differential operator method and separation of variables method, heat and wave equation in one dimension and Laplace equations in two dimensions and in polar coordinates.