Depending which field you'll want to end up in, one must remember that even the titans of the 20th century are starting to gather dust. Of course, it doesn't mean that one shouldn't be a generalist nor ignore the powerful inspiration of those who have come before us. Physics, especially foundational physics, requires a strong background in mathematics, and to be a paradigm starter nowadays, one needs a very pure background unless you "discover" something, aka experiment/observe.
When it comes to a programme such as Landau's you have to have at least some exposure. They're useful for grounding what you might have already learned in terms of introductory mastery. So let's say you did want to become a generalist (I do too albeit in "unfashionable" fields lol), then in my 11 years of physics education (7 as Undergrad+Masters), what I have done is this:
1. Introductory Books-Beginner: This could mean popsci books (Brian Greene, Lee Smolin, Hawking's Universe in a Nutshell) to AP Physics C prep to gather some exposure to what's been done and so on. For the maths involved I suggest Morris Kline's "Calculus- A Physical and Intuitive Approach," which is a life saver in AP and undergrad calculus courses.
2. Introductory Books-Intermediate: This is where one begins to do some heavy lifting with mathematical wizardry. Some of the fields you will encounter at this level in physics are vector analysis, linear algebra, complex analysis, numerical methods (very important for computing and solving ungodly equations), (partial) differential equations and Analysis (Real and Complex). Now the textbooks used here are legion, so it'll depend how you learn (as in analytical, intuitive, etc). When I was an undergrad I was practically a triple major (Engineering, Physics, Math) so I took everything that I could. What helped me along the way were some of these books:
Budget- Dover Books: Probably the best place to get some books for fields that haven't really needed to change in years. The books that carried me apart from the textbooks were Joos- Theoretical Physics; Mathematics of Classical and Quantum Physics, Fermi's Thermodynamics, Korn and Korn's Mathematical Handbook; Bohm's Quantum Physics, Messiah's Quantum Mechanics (Built way too much character with this one but helped me in grad school); and a few others I don't remember at the moment.
Budget- Schaum's Guide to ____: These are a lifesaver, especially if the books you have gloss over the niceties of computation or decide to hand waive with intuition. One must have the Mathematical Formulas regardless; the other texts are great supplements for different fields that you're getting into (my favorites being Complex Analysis, Vector Analysis, and (the new) Tensor Calculus).
Textbooks- Undergraduate: These are what professors will use in their classes and are usually listed in their syllabi. There will be variation but the content is usually the same. The books that personally took me to a higher level (at least in terms of understanding) were:
Intro Physics: Knight Physics for Scientists and Engineers
"Modern" aka Special Relativity, Baby Particle, and Intro Quantum- Tipler
Classical Mechanics- Marion and Thornton
Electrodynamics- Griffiths, this a name you'll hear a lot since he typically provides sound intuition with backing mathematics
Quantum Mechanics- Griffiths, again. Both of his books provide a solid background at the undergraduate level
Thermodynamics- Blundel and Blundel- Concepts in Thermal Physics, probably the best books I've ever read and introduced me to one of my favorite fields known as Nonequilibrium Statistical Mechanics
Mathematical Methods- Most people swear by Boaz's Mathematical Methods but at my Uni we built a lot of character using Arken's tome. Again, like Messiah, was helpful in grad school.
You might notice that I left out some classes like General Relativity, Condensed matter, and etc- well I didn't have those at my school, it's a small private college but doesn't mean I didn't research those things myself. I'll write more about those in my "bridge" section.
Now these are all hunky doory by themselves but most of the time you'll have to take prerequisite math courses to make sure you're prepared to prevail. So these are typically:
Calculus 1-3- Intro level is like Kline, Stewart onto Spivak (classic and a bridge to Analysis)
Linear Algebra- Larson's Elementary Algebra
Differential Equations- This can go either way, I personally enjoyed Dover's "Ordinary Differential Equations" but schools usually have good picks
And so on. I know, I left out real analysis, numerical methods, complex analysis, and Probability and Statistics (this is probably the most important as a modern physicist) but one can look up full courses on Youtube from the Indian Institute of Technology for several courses that address these subjects quite well.
At this point Susskind and Feynman will be helpful as guides along your journey (like Virgil with Dante). At this point one must bridge the chasm between undergrad and graduate works.
Classical Mechanics- Taylor
E/M- Franklin's Electromagnetism
Quantum- Shankar
And so on. I feel you might not be interested in more these lists so I'll stop here (which in a way is halfway). My personal fields of research are turbulence, quantum field theory, nonlinear dynamics, and differential geometry along with a floundering interest in TOEs (like String theory and the sort). I will say should you find yourself looking at the behemoth known as QFT, Blundel's QFT for the Gifted Amateur fills in so many blanks that many others have left out (seems to pair well with Zuber and Zee, like interlocking gears)
Landau's Courses are wonderful as both bridge and graduate texts, my favorites being Fluid Mechanics, Stat Physics I and II, and Physical Kinetics (the one usually forgotten). They are heavily condensed and sometimes for every page of reading is like 4 pages of derivation (which usually occurs when the the dreaded words "It can be shown" appear).
As a TLDR- It is important to have an underlying direction of where you want to end up at some point in your physics journey. I began (and still am) a generalist but now focused on the fields I mentioned. At the same time it is good to know the stages and history of physics to how it has developed today, so as a means to help you on your journey, these are the typically sequences of learning for these fields to help you get started.
Classical Paradigms- Newton- Three Laws, Forces, Gravitation, Interaction; Lagrange- Energy-based formulation, Variational method (Optimized aka Min or Max); Hamilton- Momentum-based formulation, introduction to phase and configuration space; Hamilton-Jacobi- Precursor to Quantum Mechanics, focus on "Action" and leads to a wavelike formulation of mechanics
Quantum Paradigms- Old Quantum (Planck, Einstein, Bohr, and friends): Observation of discrete units of energy and mass as opposed to a continuum, development of energy levels, and hydrogen atom along with scattering experiments and Photo-electric effect; 2nd Gen (Schroedinger, Heisenberg, Madelung, de Broglie, and friends): Introduction of uncertainty and indeterminism into physics (not completely true because of the n-body problem but this is an important shift), Copenhagen interpretation, Matrix and Wave Mechanics, Madelung fluid (pretty cool imo); 3rd Gen (Dirac, Feynman, Schwinger, Yukawa, Yang-Mills): Antimatter, Dirac Sea, QED, and a plethora of other things. As history advances, contributions and ideas explode practically exponentially, so decided to stop there.
Relativistic Paradigms- Galilean (Regular Day to day transformations, think of a passing car); Special Relativity- Length Contraction, Time dilation, Speed of Light Limit Space and time fused into a 3+1 spacetime manifold, intertwining the two; General Relativity: Curvature of Spacetime, Tensor analysis rendering equations invariant, Cosmological constant, Gravitational lensing and waves, Black holes, and frame dragging; Numerical Relativity- Alcubierre (warp) drive, 5D gravity, Colliding black holes and other ultramassive objects; Quantum Gravity: Loop Quantum, Causal Dynamical Triangulations, String Theory, QFT in Curved Spacetime, Planck Resolution
I do hope that this serves as a kinda foray into the world of physics, at least what I've experienced with it. There is more to write but I could probably write a book about it haha. I wish you the best on your journey and hope that you look upon this mountain range as a something to be taken over and never get discouraged when you leave its summit to climb its peaks.
