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.

**Classical/Analytical Mechanics:**

- 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.

**Electromagnetism: **

- Level 1: Electricity and Magnetism by Purcell
- Level 2: Introduction to Electrodynamics by Griffiths
- Level 3: Classical Electrodynamics by Jackson

**Thermodynamics: **

- 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 Mechanics: **

Statistical Physics by Mandl. Not only is it a great book but as aforementioned, it develops the subject smoothly with thermodynamics.

**Quantum Mechanics: **

- 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.

**Optics:**

- 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

**Fluid Dynamics:** Elementary Fluid Dynamics by Acheson

**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