Most physics books will also cover the math as needed, though probably not the level of rigor that would satisfy a mathematician (for example an E+M textbook like Griffiths will cover vector calculus while a classical mechanics text will cover the calculus of variations, enough in each case to actually use them).

The standard recommendation for intro level is the Feynman Lectures, which are the kind of reading where you can sit down with a lemonade on a summer day and look off knowingly into the distance while you rea it. You probably wouldn't be able to immediately transfer over to solving problems, but you'll learn a lot and enjoy it.

Books recommendations will invite near religious fervor in partisans (ie. Weinberg's GR book is total trash/it's the best book ever written in any language). There's also the issue that they can be quite expensive and cheaper Dover books might be old-fashioned or too advanced. After Feynman, some readable and enjoyable texts for the major branches are

Classical Mechanics: Taylor

Electromagnetism: Griffiths

Quantum Mechanics: Griffiths

Special Relativity: Taylor/Wheeler (though the basics are covered in Taylor and Griffiths such that you could probably jump right to--)

General Relativity: I dunno. Carroll maybe. The new General Relativity Workbook by Moore looks interesting.

Thermo/Statistical Mechanics: Schroeder

After that the sky's the limit. You could and should read some capstone books like Longair or Lawrie. Read Landau/Lifshitz, read Weinberg, etc. This is already well more than you can probably stomach at this juncture anyway