I am sure this has been discussed a lot here since this is a physics forum. But I want to make a list of what I think is good if you want to learn them. Elementary 1)Partial Differential Equations and Boundary Value Problems with Fourier Series. This book is as simple as it gets. So even if your Ordinary Differential Skills and your knowledge of Fourier Series are poor then this is a maximal ideal. Kind of Expensive. 2)Analytic Methods for Partial Differential Equations. This is another good book as a basic introduction. It explains the common techinques of solving PDE's: charachteristics, seperation of variables, integral transforms, Green's functions with fully worked out examples. Cheap. Medium 3)Partial Differential Equations: An Introduction. This book does not live up to its name, meaning this should avoid this unless you are good in analysis. It is recommended to read this after having developed a techinque for solving these equations. Way too expensive. Advanced 4)Partial Differential Equations (Evans). I have never studied the theory of PDE's, and I am sure most physicists do not need to learn it, but in case you are interested. Note: it is not completely fair for me to recommend this because I never studied the theory of PDE's. But from people I spoke this book was much recommended.