Learning a subject involves many pedagogical choices that can be difficult before knowing the field well. Here, I have laid out some of my personally favorite books in each field.
A Note: My general style of learning and taste in books favors highly formal and systematic treatments for the most part. As a result, many books I recommend will be of this style including the more applied fields like thermodynamics (Callen’s book). I do however think though that even in those more applied contexts, I find this formal approach very useful but feel free to decide yourself!
General Physics at a High School Level: Fundamentals of Physics by Halliday Resnick
A nice taste of many different fields and what is to come.
- Level 1: Introduction to Classical Mechanics by Morin
- Level 2: Classical Mechanics by Goldstein
- Level 3: Mathematical Methods of Classical Mechanics by Arnold
Also a great chapter on some basic analytical mechanics at the start of Fundamentals of Quantum Mechanics by Shankar.
- Level 1: Electricity and Magnetism by Purcell
- Level 2: Introduction to Electrodynamics by Griffiths
- Level 3: Classical Electrodynamics by Jackson
- Level 1: Equilibrium Thermodynamics by C.J. Adkins
- Level 2: Thermodynamics and an Introduction to Thermostatistics by Callen
Adkins is a great standard textbook for a regular intro course on thermodynamics. If you are really hardcore and want to witness the true power of thermodynamics, I would highly recommend Callen’s book though.
If you want to see how it really connects with statistical mechanics, I would recommend reading Statistical Physics by Mandl.
Statistical Physics by Mandl. Not only is it a great book but as aforementioned, it develops the subject smoothly with thermodynamics.
- Level 1: The Physics of Quantum Mechanics by Binney
- Level 2: Quantum Mechanics by Messiah
Before starting any quantum mechanics, I’d highly recommend reading the intro chapters of “Fundamentals of Quantum Mechanics” by Shankar up to his chapter on the postulates. I think this sets you up really nicely.
Also, I think there are a lot of interesting discussions in Quantum Mechanics by Messiah that I would recommend reading even at an introductory level. A notable topic is that of the spectrum for one-dimensional problems.
- Level 1: Optics by Hecht
- Level 2: Principles of Optics by Born and Wolf
Hecht is admittedly a little wordy but worth the read to gain knowledge and context for many optical situations. Born and Wolf however is a thorough rigorous treatment of the subject which makes strong connections to the underlying electromagnetism.
Linear Algebra: These Lecture Notes
Waves: Wave Motion Chapter in Optics by Hecht
Financial Mathematics: http://www.math.ntu.edu.tw/~chern/notes/finance.pdf
Functional Analysis: Introductory Functional Analysis with Applications by Kreyszig
Highly Recommended Lecture Series for the Mathematical Physicist: Geometrical Anatomy of Theoretical Physics