While I was looking for information on the Lewy equation, I found some introductory material on PDEs:

- Lectures notes by T. W. KÃ¶rner
- Lecture notes by Joshi and Wassermann
- The course page for Methods of Numerical Simulation in Fluids and Plasmas, which includes a detailed notes on PDEs.
- The course page for Computational Methods, which includes lecture notes on PDEs and other topics.
- An essay on PDE as a unified subject