
The fundamental goal of the [book] is to provide a broad, rigorous, yet accessible introduction to calculus-based physics... There is plenty of material for an intensive three-semester or five-quarter course.-Pref.
The standard text to build understanding in physics is University Physics by Sears & Zemansky.
It's worth remembering you're quite far from the ground in physics, and it's mostly taught with "neat" cases that give insight into physics. I.e. the thought experiment to show why kinetic energy must scale quadratically with velocity is carefully designed to show that conclusion. You shouldn't expect to have come up with it off the cuff.
- University Physics by Young and Freedman
- Fundamentals of Physics by Halliday, Resnick, Walker
- Modern Physics by Krane
You might guess that real physics is not actually in freshman textbooks, and you are right. Modern physics requires rigorous mathematics.
For a nonrigorous introduction/overview:
- The Road to Reality by Roger Penrose
If you want to actually learn almost all of physics at a high level:
- Course of Theoretical Physics by Landau
Note that Landau is extremely difficult.
If you want to learn the math needed for modern physics (topology) in the context of physics, nonrigorously:
- Geometry, Topology, and Physics by Nakahara
I think the most important advice is don't try to skip ahead. It's tempting to jump straight into the cool modern physics topics like quantum mechanics and general relativity before you have the necessary background. I've gone down that route and didn't really learn anything that way.
If you haven't taken any physics at the university level, you probably want to start with one of the big calculus-based intro books like Young's University Physics. Calculus, differential equations, and linear algebra are really important, so you might want to pick up separate textbooks on those (or a single volume Engineering Mathematics textbook) unless you have already learned these subjects. Everyone speaks highly of the Feynman Lectures, but some say that they're only really beneficial after you already have a decent understanding of the subjects being covered. I believe I heard Sean Carroll say this once on a podcast, and I trust his opinion on physics matters.
The core subjects in undergraduate physics are classical mechanics, electrodynamics, special relativity, quantum mechanics, and statistical mechanics/thermodynamics. You will learn all of these subjects from an intro textbook as a first pass. After that, you'll return to each subject and essentially relearn it at a more advanced level with dedicated textbooks for each (except SR which is covered in electrodynamics). General relativity and quantum field theory are usually taught at the graduate level or as upper-level undergraduate electives, so those are best to save for last.
Having forgotten a lot of the math I learned a decade ago, I've found that having one of those Mathematical Methods books nearby at all times is indispensable. I went with Riley/Hobson/Bence, but Boas also gets good reviews. These books are a bit terse if you're learning a subject for the first time, but they're great as a reference and contain pretty much all the math you will ever need to know unless you plan on doing research-level physics.
Don't forget about YouTube. There are lots of lectures available from top universities, as well as independent content creators. I haven't looked much into physics channels yet, but on the math side I highly recommend 3Blue1Brown, especially his series "Essence of Calculus" and "Essence of Linear Algebra".
This is a good roadmap to guide your study path and has good textbook recommendations: https://www.susanrigetti.com/physics
"University Physics" by Francis Sears and Mark Zemansky "Introduction to Electrodynamics" by David J. Griffiths "Electricity and Magnetism" by Edward M. Purcell
May I suggest a good book on first year physics?
https://www.amazon.com/s?k=Sears+%26+Zemansky%27s+University...
I used a much earlier edition almost 40 years ago, when I took my first university physics class. As far as I know, the fundamentals have not changed.
This would be a good investment if you really want to understand.
Your immediate goal should be to get a firm grounding in classical physics, which will be important for everything else you do. When choosing a textbook, the most important thing is to pick one that's aimed at scientists and engineers. That means it should be calculus-based, "algebra-based physics" being a contradiction in terms. If you don't know calculus, you should start there. (This will set you back some more money. Sounds like a plan for Christmas, Hanukkah, etc.)
To my knowledge, none of the introductory texts are truly great, but I did some poking around and University Physics by Young, Freedman, and Ford looks like a good bet. If you need to learn calculus, Calculus by Larson and Edwards looks decent. Get the most recent editions if you can afford them, but I'm sure older editions are fine. Those two books alone should take you a year or two to consume, and they are likely to be very challenging unless you have an exceptional preparation in mathematics. But even if you get stuck occasionally, you'll still be way ahead of the curve. (I wish someone had put a calculus-based physics textbook in my hands when I was in high school. I would have been unstoppable. Unfortunately, though it now seems impossible, I went to high school before Amazon or even the Web, so it simply never occurred to anyone.)
I recommend supplementing the textbooks with liberal use of Khan Academy videos and Wikipedia articles. More than anything, it is essential to solve a large number of exercises. Developing a good physical intuition is important, but physics is a quantitative discipline, which means being able to do calculations.
One more thing: if you want to demonstrate your competence to the world (and to college admissions committees), it's a good idea to take the AP Physics exam (B or C) at some point. The AP Physics C exam is the best one to target if you only have enough time to take one, as it will let you test out of introductory courses at many schools. (Not at Caltech though—we have a separate system of placement exams.) Take a look at the AP Physics C website to see the syllabus. If you decide to take the exam, buying a test-prep book such as 5 Steps to a 5 AP Physics B&C is probably a good idea. If you go this route, try to negotiate with your school to get course credit for your independent study.
P.S. At some point, read The Feynman Lectures on Physics. FLP doesn't make for a good introduction, but after you have a foundation it's gold.