Inspired by How should a physics student study mathematics? and in the same vein as Best books for mathematical background?, although in a more general fashion, I'd like to know if anyone is interested in doing a list of the books 'par excellence' for a physicist.
In spite of the frivolous nature of this post, I think it can be a valuable resource.
Course of Theoretical Physics - L.D. Landau, E.M. Lifshitz.
Mathematical Methods of Physics - Mathews, Walker. Very nice chapter on complex variables and evaluation of integrals, presenting must-know tricks to solve non-trivial problems. Also contains an introduction to groups and group representations with physical applications.
Mathematics of Classical and Quantum Physics - Byron and Fuller.
Topics in Algebra - I. N. Herstein. Extremely well written, introduce basic concepts in groups, rings, vector spaces, fields and linear transformations. Concepts are motivated and a nice set of problems accompany each chapter (some of them quite challenging).
Partial Differential Equations in Physics - Arnold Sommerfeld. Although a bit dated, very clear explanations. First chapter on Fourier Series is enlightening. The ratio interesting information/page is extremely large. Contains discussions on types of differential equations, integral equations, boundary value problems, special functions and eigenfunctions.