This is a two-semested introductory PDE course. The only prerequisities are some knowledge of muldi-dimensional calculus and elementary ordinary differential equations. The course will start by the study of basic PDEs, such as the Laplace equation, the heat equation, and the wave equation. More general classes of equations will be covered subsequently. Various approaches will be explained, both classical and modern. The exposition will include some of the relevant parts in the Theory of Distributions and the Fourier Transformation. The course will use no official texbook, but I will distribute some notes. Also, a list of suitable literature will be supplied. There will be three homework assignments during each semester. The final grade will be based on the homework assignments.