Introduction to string theory

Mathematical rigor is not the most important thing when first learning strings, there are many things that are not possible to formulate rigorously, because the best language for doing this isn't known. In addition to Polchinsky (which is excellent), I recommend reading Green Schwarz and Witten, and also the original papers, since these have points of view which are not found in later articles, but are profound and important.

These are found in two very good reprint volumes: "Dual Models", and "Superstrings" (although much of vol II is well covered in Green Schwarz and Witten and Polchinsky). These are essential for properly understanding the subject, even today. The issue is the Regge ideas and the S-matrix ideas which are glossed over in later treatments.

The canonical textbook is the two-volume set by Polchinski. David Tong has very nice notes up following this text.

You should be able to find various review articles on the arXiv as well, for instance:

• T. Mohaupt, "Introduction to String Theory", arXiv:hep-th/0207249.

• R. J. Szabo, "BUSSTEPP Lectures on String Theory", arXiv:hep-th/0207142.

Hope that helps...

Some standard sources:

• Both books by Schwarz -- GSW and BBS. BBS of course is more updated on recent developments, both books are quite in-depth short of reading original research directly.
• Kaku, "Strings, Conformal fields and M-theory" is a mathematically rigorous course. Perhaps quite surprising for those readers only with experience with Kaku the populariser.
• McMahon's "String theory demystified" is not exactly the most insightful or in-depth book, but it's broad, and can be used as a general list of stuff to study in the theory.

Lecture notes I've looked at --

• Mohaupt has a limited scope and depth, but covers the gravitational implications.
• Wray
• Szabo

Also for string field theory -- [1], supposedly better version at [2] [PDF].

Shiraz Minwala's lectures -- suggested by Larry Harson in the comments.