Math and Theoretical Physics Topics & Textbook for Self-Study I am from Singapore, a civil engineering graduate and I've graduated from university in 2009.
Throughout my school days I've been interested in Physics, unfortunately I was not accepted into the local university as my grades did not match up. And I couldn't afford to study abroad. Hence I took up whatever was offered to me at that point; civil engineering.
Right now, I'm on a mission to self-study theoretical physics so that I can fully appreciate the beauty of it; I mean right down to the deep mathematical level of it. I am particularly interested in the subjects: General Relativity, Quantum Theory, M-theory. I acknowledge that first of all I'd have to master the math before I can delve deeper into the theoretical physics subjects.
I would like to ask forumers the following questions:
(1) - May I know what are the sequence of math & physics topics I have to master? I mean in a step-by-step way starting from high school level knowledge.
(2) - Could you recommend texts both from the math & the theoretical physics side? Based on my research I have shortlisted a few and they are 
(a) Introduction to Mathematical Physics: Methods and Concepts by Chun Wa Wong. 
(b) A course in theoretical physics by P. john Shepherd 
(c) Introduction to Modern Physics: Theoretical Foundations by John Dirk Walecka & 
(d) A Unified Grand Tour of Theoretical Physics, Third Edition by Ian D. Lawrie.  
Are these books suitable and good for my cause? What other textbooks do you all recommend? I am willing to self-study patiently even if it takes me 10 years.
 A: Pick a topic, goto wikipedia/mathworld page. There are book listed at the end, Select what you like and start reading. If not satisfied, just google it or like John said PSE has good book recommendations too. You can also try the books listed in References section in any popular physics paper. You can search arxiv or google scholar for a particular field. One often cited set of books is Course of Theoretical Physics by Landau so be sure to read it.
The other approach would be study from undergraduate courses and graduate courses. Google for a particular courses. However this is very mundane approach. Instead you can read a 'for general public' book, get motivated and then read more technical books.
A: I would highly recommend "Quantum Physics of Atoms, Molecules & Solids" by Eisberg and Resnick. It covers so many topics and will give you a good grounding in quantum mechanics if you give it time. It also has lot's of sections on many other topics which serve as a good introduction. It's widely considered to be one of the best books on general physics available. 
If you're an engineer than your understanding of mathematics and mechanics, both very fundamental, should be a good starting point for learning physics. I think you should start out by trying to understand the following experiments and discoveries before tackling university level courses: 
Young's double slit experiment
Photoelectric effect
Blackbody radiation
Wave-particle duality 
Heisenberg uncertainty principle 
These are typically what a first year undergraduate physicist must understand before they go on to learn proper quantum mechanics. There are also lot's of great university courses which are free on sites like Coursera and EdX. I think these will be the best way to learn physics. 
