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I am extremely interested in GR, but somehow feel that the books I read are not really enough. Frankly, I find many question on this site and elsewhere completely bewildering, which makes me think that I don't have a solid foundation, especially in classical mechanics and various mathematical techniques. Here's a list of books I have read:

MATHEMATICS(After pre calculus and basic calculus)

Mathematical methods for physicists(Still working my way through) By Arfken and Weber

Advanced calculus by David Widder

Ordinary differential equations by Coddington

Principles of mathematical analysis by Rudin

Vector Calculus

Tensor calculus by Barry Spain

RELATIVITY

Introduction to special relativity by Resnick

Gravity by Hartle

General relativity with applications to astrophysics by Straumann (newly acquired)

I have a few books on dynamics, nuclear physics, etc, but they are quite unnecessary. I am not much into QM, and have only read Griffith's. I also have, as a reference, PRINCIPLES OF PHYSICS by Resnick and Walker.

All my knowledge of classical mechanics and lagrangian formulism is from pdf versions of Feynman's lectures. Please suggest me some books that will fill the gap I have left out. Just to be clear, I want to read Mathematical theory of black holes by Chandrahekhar next, so I want to know where I need to improve.

NOTE: I am still in high school, and I don't have any professor to help me out, so the books should be suitable for self study. All the same, they should be properly rigorous.

EDIT: I am not very comfortable with the exercises suggested in most of the books (esp. Mathematical methods for physicists and both the GR books. Though I have no conceptual glitches, I really want to be able to solve the exercise problems, as doing so is both satisfactory and rewarding. Any suggestions on that( how to be more efficient)? Am I going too far too soon, and maybe need to stop down and consult a book which will perhaps give me a good foundation to solve the exercises, or a book with excellent exercises? If so, which one? 2: Of course, I have viewed the lectures by Susskind.

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marked as duplicate by David Z Oct 25 '14 at 10:31

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    $\begingroup$ @Mostafa, I am not STARTING with GR, I just feel I have left a gap in my prerequisites before starting, which i did. ( check my edit) $\endgroup$ – GRrocks Oct 25 '14 at 10:10
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    $\begingroup$ if i may add, having the necessary mathematical background and concepts in place is certainly sth that will make the language of GR accesible and manageable. BUT the main point of GR is the physics. WHY would sth like GR be needed to formulate gravity or frames of reference, WHY not just Newton's gravity? WHAT was the physical problem that GR tried to solve by using the (mathematical) formulation known as Tensor analysis and Riemannian manifolds? These are NOT answered by (just) the math (BUT they certainly help to formulate and understand the answer) $\endgroup$ – Nikos M. Oct 25 '14 at 10:45