This page lists literature on string theory.
(See also at string theory FAQ.)
There is to date no textbook on string theory genuinely digestible by the standard pure mathematician. Even those that claim to be are not, as experience shows. But here are some books that make a strong effort to go beyond the vagueness of the “mainstream” books, which are listed further below.
Miranda Cheng, Mathematical tools for string theorists, lecture notes 2013 (pdf)
Pierre Deligne, Pavel Etingof, Dan Freed, L. Jeffrey, David Kazhdan, John Morgan, D.R. Morrison and Edward Witten (eds). Quantum Fields and Strings, A course for mathematicians, 2 vols. Amer. Math. Soc. Providence 1999. (web version)
This is a long collection of (in parts) long lectures by many top string theorists and also by some genuine top mathematicians. Correspondingly it covers a lot of ground, while still being introductory. Especially towards the beginning there is a strong effort towards trying to formalize or at least systematize much of the standard lore. But one can see that eventually the task of doing that throughout had been overwhelming. Nevertheless, this is probably the best source that there is out there. If you only ever touch a single book on string theory, touch this one.
This focuses on the discussion of supergravity-aspects of string theory from the point of view of the D'Auria-Fre formulation of supergravity. Therefore, while far, far from being written in the style of a mathematical treatise, this book stands out as making a consistent proposal for what the central ingredients of a mathematical formalization might be: as explained at the above link, secretly this book is all about describing supergravity in terms of infinity-connections with values in super L-infinity algebras such as the supergravity Lie 3-algebra.
Hisham Sati, Urs Schreiber, Mathematical Foundations of Quantum Field and Perturbative String Theory, Proceedings of Symposia in Pure Mathematics, AMS (2011)
This volume tries to give an impression of the rather recent massive progress that has happened in the mathematical understanding of fundamental ingredients of perturbative string theory, revolving around the proof of the cobordism hypothesis and related topics of higher category theory and physics. This is not an introductory textbook, even though some contributions do contain introductory material. Rather, this is meant to be read by people who already understand the basic idea of string theory and would like to see what the mathematical picture behind it all is going to be.
Igor V. Dolgachev, Introduction to string theory
(rough survey for laymen)
Barton Zwiebach, A first course in string theory, Cambridge University Press (2009)
(meant to be a course for undergraduates)
Michael Dine, Supersymmetry and string theory: beyond the standard model, Cambridge University Press 2006, 2007
Alexander Polyakov, Gauge fields and strings,
Brian Hatfield, Quantum field theory of point particles and strings, Frontiers in Physics, 752 pages, Westview Press 1998
Clifford Johnson, D-branes
Richard Szabo, An introduction to string theory and D-brane dynamics
Кетов С.В. “Введение в квантовую теорию струн и суперструн” djvu
E. Alvarez, P. Meessen, String primer (hep-th/9810240)
David Tong, Lectures on string theory (arxiv/0908.0333)
Brian Greene, The elegant universe: superstrings, hidden dimensions, and the quest for the ultimate theory
Michio Kaku, various volumes
video and slides of Witten’s KITP overview Future of String Theory
Hisham Sati, Geometric and topological structures related to M-branes, comprehensive survey
Anton Kapustin, D. O. Orlov, Lectures on mirror symmetry, derived categories, and -branes, Russian Mathematical Surveys, 2004, 59:5, 907–940 (Russian version: pdf, [arxiv version: arxiv:math.AG/0308173).]