Thomas, J.W., "Numerical Partial Differential Equations - Finite Difference Methods", Springer-Verlag, 1995.

A comprehensive book on the topic of Numerical PDE. I love the detailed mathematical explanations on each concepts, which give very logical and structured explanations from the first page to the last page of the book. Details in the computing sections are also very useful for us to understand some 'strange' things that results from computations.