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.

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.

I love this thesis paper: A Detailed Introduction to String Theory by Andy Svesko.

The last chapter of Geometry, Topology and Physics by Nakahara is a relatively rigorous introduction to the path-integral quantization of Bosonic string theory.

I personally benefited from both Nakahara and Polchinski's String Theory Volume 1. As for me, Polchinski's book is very challenging to read, but it is the most clear and well-organized book in string theory.

I don't know anything about F-theory, string field theory and matrix theory, but these two books have very clear introductions of the path-integral quantization of Bosonic string theory.

I happen to like "D-Branes", by Clifford Johnson.

There are different ways to learn string theory. Starting with a classical string and quantizing is not always the best way. The reason is that string theory is not actually a theory of strings or mesons, it is really a theory of quantum gravity. Another approach is to learn the massless bosonic sector of the different string theories. These are described in Becker, Becker & Schwartz, for example. Then go back and see where they come from from the string perspective.

Polchinsky is great once you already have a feel for what's going on.

String theory is one of those things that's hard to teach because we're not really sure what it's a theory of. But it has quantum gravity which is good.

To the cited reviews and books I would also add the lecture notes by Timo Weigand (https://www.thphys.uni-heidelberg.de/~weigand/Skript-strings11-12/Strings.pdf) which are quite pedagogic and complete for a first course and also the book "Basic Concepts of String Theory" by Blumenhagen, Luest and Theisen (https://www.springer.com/de/book/9783642294969) which contains to my understanding more explicit computations and has some very nice points appart from being quite recent (2008), I have learned firstly from it and I like it, maybe the lenguage is not so envolving like Polchinski or GSW but to my understanding contains more details and the structure of the book is more adapted to our time. Of course, the other references are well known and very good also but I just wanted to add these two German references that usually are not so well known out of Europe, but for me are quite good.

There's always David Tong's notes on string theory. If you really want to get the ideas and move forward then it's the place to go. If you really want to take a stroll through string theory (and not in a hurry) then Polchinski is something you should definitely look.