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What would be good introductory and follow-up references to understand the close ties between physics and geometry.

I'm a retired engineer with the math background to handle Shankar's Principles of Quantum Mechanics, but like most engineers my era, I know little of the fundamentals of set theory, group theory, topology, etc. Although you can't help picking up bits and pieces following a self-education route.

I guess I'm looking for an efficient roadmap through at least the critical fundamental theories/types of mathematics and physics that leads to a reasonable level of understanding of how calabi-yau manifolds generate/correspond to a particular physics. (Pardon my lack of proper terminology.)

Ideally, references would be aimed at newcomers, but not at an elementary level. And, as an engineer, it's nice to find a text that introduces the concepts first and then dives into the math.

This is my first time on this site. If I've misunderstood the nature of the questions allowed, I apologize.

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closed as too localized by David Z Jun 8 '12 at 5:34

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Hi Mike, and welcome to Physics Stack Exchange! We tend to keep a tight lid on these book recommendation questions, so to speak - they're not really the kind of thing this site was designed for. I'd suggest you have a look at physics.stackexchange.com/questions/12175/book-recommendations and see if anything there would be useful to you. (Please don't feel that you've done anything wrong, by the way! We don't hold a closed question or two against you at all, and I do hope you'll feel welcome to keep contributing here.) –  David Z Jun 8 '12 at 5:37
    
Okay. Thanks David. –  Mike Jun 8 '12 at 5:48