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Which are the best introductory books for topology, algebraic geometry, differential geometry, manifolds, etc, needed for string theory?

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Before answering, please see our policy on resource recommendation questions. Please write substantial answers that detail the style, content, and prerequisites of the book, paper or other resource. Explain the nature of the resource so that readers can decide which one is best suited for them rather than relying on the opinions of others. Answers containing only a reference to a book or paper will be removed!

marked as duplicate by Manishearth Feb 14 '13 at 19:34

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

    
Possible duplicates: physics.stackexchange.com/q/193/2451 and links therein. – Qmechanic Feb 14 '13 at 19:05
    
1. Intro to Smooth Manifolds - Lee 2. Riemannian Geometry and Geometric Analysis - Jost 3. Complex Geometry: An Introduction - Huybrechts 4. Algebraic Topology - Hatcher 5. Algebraic Geometry - Hartshorne – Jake Apr 2 at 21:18