How does a Masters student of math learn physics by self? I am a Masters student of math interested in physics. When I was an undergraduate, I took the introductory course of physics, but it is just slightly harder than high school physics course. To be precise, it just taught us how to use calculus in physics, without involving the higher knowledge of math such as manifold, PDE, abstract algebra and etc. By the way, the knowledge in that course is "discrete", the connections between fields of physics is omited.
My question is, what I should do to learn "real physics" by myself? What books or materials should I read?
 A: I think it's not difficult to find physics books explicitly written for mathematicians. For instance, Takhtajan's "Quantum Mechanics for Mathematicians" or "General relativity for mathematicians" by Sachs and Wu.
But I personally think you should start by familiarizing with experimental physics. The classical "Atomic Physics" by Max Born can be a good read before anything more formal, for instance.  Also, if you are interested in classical electrodynamics, I would recommend "Classical electricity and magnetism" (another old one, 1960s...), by Panofsky and Phillips, for similar reasons. The energy associated with the EM field, for instance, is treated with an experimental attitude which is useful, I believe, to have a better grasp on the physical meaning of energy conservation involving EM phenomena. Special relativity is also introduced with attention to its experimental basis.
In this way you may add depth, in a dimension otherwise hardly accessible, to your mathematical understanding.
A: The Feynman lectures on physics would also be a suitable entry point.
A: For more advanced stuff written by mathematicians, Lectures on Quantum Field Theory by Borcherds, Quantum Fields and Strings: a course for mathematicians (well, easier parts of it, probably - this is a two-volume set!), and, more broad and accessible, written by a rare universalist (that is, physicist but also mathematician), The Road to Reality: A Complete Guide to the Laws of the Universe by Penrose.
A: Some excellent books for mathematicians who begin to study quantum mechanics are
Alexander Givental, Introduction to Quantum Mechanics (available from the author for a very modest price).
L. D. Faddeev and O. A. Yakubovskii, Lectures on quantum mechanics for mathematics students. Translated from the 1980 Russian original by Harold McFaden. With an appendix by Leon Takhtajan. Student Mathematical Library, 47. American Mathematical Society, Providence, RI, 2009.
On classical mechanics, I recommend L. Landau and E. Lifshitz, Course of theoretical physics, vol. I, and, of course,
V. Arnold, Mathematical methods of classical mechanics.
A: I would suggest Mathematical Methods of Classical Mechanics by V.I Arnold, it does not go over any quantum mechanics discussions, but keep in mind that our intuition to do things like quantization arises from classical concepts.
A: I recommend strongly against Leonard Susskinds theoretical minimum. It's written for people who have very rudimentary knowledge not one who has already a bsc in math.
Let me give you some pretext. Pretty much everything in Physics is somehow related to the ideas in Differential Geometry. So having good knowledge of this will help.
Now, for the actual book, Roger Penroses Road to Reality
This book introduces a lot of the Differential Geometry pre requisites and does classical , quantum and relativistic physics in its context.
I really liked this book and I firmly believe that one can get quite far if they are to simply understand all the ideas in the book.
The issue with this book it doesn't teach at all to calculate stuff. You can check out Kai S Lams classical mechanic book for this
A: What kind of physics are you interested in? If you are interested in rigorous introduction to statistical physics, there are classic references such as Grimmett's random cluster model textbook, Yvan Velenik's statistical mechanics textbook, or Duminil-Copin's lecture notes on the Potts model.
If you want a more non-rigorous (i.e. more real-physics flavor) approach to modern statistical physics, John Cardy's RG textbook is good, but I have to warn you the treatment of disordered systems in Chapter 8 is highly non-rigorous and even incorrect in certain cases.
A: I can recommend Leonard Susskind's Theoretical Minimum:

A number of years ago I became aware of the large number of physics
enthusiasts out there who have no venue to learn modern physics and
cosmology.  Fat advanced textbooks are not suitable to people who have
no teacher to ask questions of, and the popular literature does not go
deeply enough to satisfy these curious people.  So I started a series
of courses on modern physics at Stanford University where I am a
professor of physics.  The courses are specifically aimed at people
who know, or once knew, a bit of algebra and calculus, but are more or
less beginners.

The name "theoretical minimum" is a reference to the notoriously rigorous exam a student needed to pass in order to study with Lev Landau. See also this discussion.
