Physics textbooks are strange beasts. An inordinate amount of effort to write, profitable only if it becomes the bible for that field, and expensive for the student. They can be a way of the great teachers of physics to pass on their wisdom, or an incomprehensible morass of algebra that serves no good purpose.
Hence, I'm posting recommendations for textbooks below, along with a short review. I will also link to useful online notes, that ought to be published as books, but their authors are happy to give away for free.
Landau & Lifshitz
Whilst the rest of the books on this page are divded by subject matter. The classic books by Landau & Lifshitz (aided later by Berestetskii and Pitaevskii) deserve their own listing. The prosaically titled Course of Theoretical Physics is in fact a masterpiece. Spanning the whole breadth of theoretical physics at a level that is accessible to a graduate student they can be some of the most useful resources on a physicists bookshelf and some of the best ways to learn a new area.
- Volume 1: Mechanics
- Volume 2: The Classical Theory of Fields
- Quantum Mechanics by E. Merzbacher
Vol 3 of L&L
Quantum Field Theory
- Quantum Field Theory by Ryder
- The Quantum Theory of Fields, Vol 1 by Weinberg
QFT Notes by D. Tong -- The course that I first learnt QFT from, a great teacher and a very lucid introduction to the field.
- Classical Electrodynamics by J. D. Jackson
Vol 2 of L&L
Vol 1 of L&L
- Mathematical Methods of classical mechanics by V.I. Arnold
David Tong's Lecture Notes here. Again, the course that I learned classical mechanics from. Good introduction, doesn't cover the advanced topics that Landau or Arnold do.
- Vol 6
- Statistical Fluid Mechanics
- Hydrodynamic and Hydromagnetic Stability
As this is my field, I've given it its own page. Includes recommendations of books, all the way up to advanced graduate student level. Also links to review papers and online notes. I've also included a list of 'books that need to be written but nobody has managed to write yet'.