How can a high school senior independently study undergraduate or even graduate level physics?

I'm currently a graduate student in physics, so I've been through much of the journey myself, though not very much on an self-taught basis, but through the university system. To continue learning physics as an autodidact, one will have to realize that physics at high school level, undergraduate level, and graduate level can really be quite different. The mastery of mathematical skills required at each level would increase as well. High school physics mainly focuses on (classical) mechanics with some introductory thermodynamics and perhaps even the most basic ideas of quantum theory. The mathematical skills required in solving the problems usually involve basic algebra and (at most) basic calculus only. At undergraduate level, physics was more of an introduction to the modern working ideas in physics for me. That includes the four main types of mechanics: classical mechanics, electromagnetism (electrodynamics),  quantum mechanics and statistical mechanics. There would be some introduction to other important topics like optics, thermodynamics and fluid mechanics. Some of the more advanced senior undergraduates may venture into nuclear physics, quantum field theory and general relativity, or branch off into other specializations like computational physics, condensed matter physics, solid state physics, biophysics, material science, fluid mechanics etc. The mathematical skills required for the most basic of those courses are mainly (single and multivariate) calculus and linear algebra (in quantum mechanics). For the advanced courses, some of the mathematical courses required are real/complex analysis, group theory (in quantum field theory) and differential geometry (in general relativity). At the graduate level, there are advanced courses at the graduate level that can help one achieve an understanding of physics broadly and deeply enough to be able to appreciate the bulk of mainstream physics. For graduate courses, the math required are mostly what is required for advanced undergraduate courses, only applied at an advanced level, like basic dough at the hands of a master baker. Beyond that, physics is somewhat like an infinite corridor. You can finally choose which area interests you the most and you can learn and consume knowledge as much as you want within that particular door you choose to enter, never knowing whether this particular door or the next one might have been a better choice. The mathematical skills required within each specialization would differ, from a mix of abstract algebra, topology and differential geometry (and much more) in string theory to complicated differential equations in cosmology. I hope the above would have given you some idea of the road ahead. Now, here are some resources that can help you along: Textbooks Undergraduate: Quantum Mechanics: Griffiths (introductory) Merzbacher Sakurai Electromagnetism: Griffiths (Introductory) Statistical mechanics: Huang Classical Mechanics: Goldstein Solid state physics: Kittel (introductory) Elementary particle physics: Griffiths (Introductory) Graduate: Landau/Lifshitz series (Series of ten books with good rigor) Jackson (Electrodynamics) Goldstein (Classical Mechanics) Sakurai (Quantum Mechanics) Peskin and Schroeder (Quantum Field Theory) 2. Online courses / Notes from universities/professors Many universities and professors are now offering whole courses on the web: http://ocw.mit.edu/courses/physics/ https://www.coursera.org/courses?cats=physics https://www.edx.org/course-list/allschools/physics/allcourses You could search for videos (http://freevideolectures.com/search?cx=partner-pub-4905108038008617%3Aorkq27-ucfp&cof=FORID%3A10&ie=ISO-8859-1&q=physics&sa=Search&siteurl=freevideolectures.com%2F&ref=&ss=1277j403659j7) or google for university course notes. Though some websites may lack answers to assignments, most should have a complete set of notes. For instance, for quantum mechanics: http://bohr.physics.berkeley.edu/classes/221/1011/221a.html There are also useful lectures by great physicists, like Richard Feynman (http://www.feynmanlectures.info/) and Sidney Coleman (https://www.physics.harvard.edu/events/videos/Phys253). David Tong has also provided a http://www.damtp.cam.ac.uk/user/tong/teaching.html at his webpage which covers much introductory ground for theoretical physics. In addition, I'd say this http://mysbfiles.stonybrook.edu/~klikharev/EGP/ by Konstantin Likharev deserves special mention. I have used his quantum mechanics course notes in his course and found them particularly helpful. It is self-contained, well written, with great rigor.   3. Other guidelines/resources: http://www.staff.science.uu.nl/~Gadda001/goodtheorist/index.html (this is an old website to be removed soon, by Gerard t'Hooft) http://www.staff.science.uu.nl/~hooft101/theorist.html (a new website by Gerard t'Hooft with lots of links to websites, textbooks and other information) http://mkaku.org/home/articles/so-you-want-to-become-a-physicist/ (General guidelines by Michio Kaku) I'd also suggest checking out university libraries/bookstores, if you have access to them. They might require paid membership if they're open to public, but they do provide a great collection of books to choose from. Some undergraduate textbooks like Griffiths are meant as an introduction to the ideas, so there might some hand waving in the equations, just to show how one might derive the eventual answer. If you want a very rigorous treatment, most graduate level texts/notes strive towards that with as much rigor as possible in a sensible manner. There are much more resources than what has been mentioned above, so do keep a lookout on amazon or check out university course websites to look at the textbooks or course notes they use. In addition, just as a side note, physics is not only about theory - it is also about being able to verify the theory with your hands (i.e. through experiments). If you're interested in becoming a physicist, it is important to get your hands dirty as well! (Or at least keep up with the general trend of progress in experiments.) Good luck, and most importantly, keep faith and enjoy the journey!

Here is an anecdotal response (at least for university-level physics): I obtained almost the entirety of both my college-level mathematics and physics via independent study, so hopefully this response will be helpful. In particular, I utilized as my primary method of study. First to gain the mathematical skills that I needed for the subject: http://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2005/ http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-spring-2006/index.htm http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/ http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/ With this background, you should have the necessary mathematical skills you need for most of your undergraduate physics education (except for perhaps some Fourier analysis and some real/complex analysis too, but you can easily pick that up later, and its probably better to actually take a course in those subjects and learn them formally anyway). You won't really need the formalization of calculus (and other mathematics taught in Spivak quite yet (although it will be useful knowledge to obtain later)), even for rigorously developed physics; it is more about the problem-solving skills you develop rather than the theory. Now we move on to learning physics. As you have noted, you have already learned basic classical mechanics and E&M, so I won't post the MITOpenCourseware links for the introductions to those subjects. The best continuation of learning those subjects would then be: Mechanics: Kleppner/Kolenkow is an excellent textbook, as is Morin. For a challenge (perhaps after completing one of the aforementioned textbook), you may want to attempt Goldstein for a very theoretical approach to classical mechanics (indeed, some would call the treatment covered in this book the foundation of theoretical physics). E&M: Griffiths is easily the best way to learn classical E&M. It has the perfect blend of problems and theory for the advanced independent learner, and gives you a very rigorous treatment of the subject. Should you wish to pursue the subject further, you can try Jackson for a graduate level version of the subject (it covers all of classical electrodynamics and introduces the reader to classical field theory). At this point it is probably a good idea to pick up some of the advanced mathematics that you will need for the formalism of Quantum Mechanics. In particular, if you have not seen a formal treatment of calculus before, it might be a good idea to work through Spivak as you suggested. In addition, you will probably want to obtain a solid understanding of real/complex analysis in order to get an intuition for Hilbert spaces. A couple suggestions would include the Princeton Lecture series (which covers Fourier analysis as well, also important to know) or Rudin. Quantum Mechanics: Despite the conventional usage of Griffiths, I would not recommend the textbook to anyone looking to obtain a deep understanding of QM. Instead, I would reccomend that you work through any number/combination of the following: Liboff, Feynman, Shankar, Sakurai (this one is a little more advanced). Another good book that I stumbled upon recently was Townsend, which I thought provided a very good introduction to the subject. Disclaimer: I have yet to get beyond this point, so anything after here is just word-of-mouth advice. At this point physics really branched out into a bunch of different directions, although what follows is a subset of the fields, along with good recommendations for learning each one. Obviously, there will also be some more advanced mathematics required for this section; in particular you will need differential geometry for general relativity, and you should probably learn some absract algebra and group theory, just because it is useful and comes up in a bunch of different ways in physics. Some topology will prove useful too, especially once you start investigating QFT and possibly string theory/M-theory. General Relativity: After attaining a sufficient background in Differential Geometry, I have heard that Carroll is a very good introductory textbook on the subject. Statistical Physics: I have heard that Landau/Lifschitz is pretty good here. You might want to try an introductory textbook first (Kittel and Kroemer is an excellent suggestion) Quantum Field Theory: Although probably not the best introduction, it is indisputable that Weinberg has the best theoretical approach to the subject. String Theory: I don't really know. I have heard that both Polchinski and Zwiebach are excellent introductions.

Have you searched http://www.cousera.org? They offer tons of free classes that you can approach at your own pace.

I myself have studied feynman lectures on physics in high school. Feynman has very nicely presented ideas without providing much of horrifying mathematics. I pretty much understood everything from his book. Most important thing is understanding physical ideas. You can learn mathematics from other books. Learning calculus will be a very good idea if you do not want to get frustated with the mathematical complications involved in some very beautiful physical ideas. For feynman lectures on physics calculus will be sufficient. After completing Feynman lectures (Part 1 and 2 especially. Part 3 is quantum mechanics and is somewhat more involved in terms of ideas and some mathematical concepts of vector space) I will suggest that you get a book named "Mathematics for physicists" . In it you will find much of interesting mathematical ideas used in physics. After completing Feynman lectures on Physics you will have enough idea of what to study next like relativity or quantum mechanics or thermodynamics. Then just google the books on that topic and enjoy your journey,