Periodic Hamiltonian Flows on Four Dimensional Manifolds Book

This is in my opinion the authoritative textbook. Volume 1 focuses on developing the worldsheet theory of the string. Polchinski also covers in detail all of the key mathematical tools and concepts, from conformal field theory to BRST quantisation and computing scattering amplitudes.

For simplicity, Volume 1 focuses solely on bosonic string theory with the fermionic theory and things like supersymmetry - hence superstring theory - reserved for Volume 2. This type of structure is generally the rule to teaching the subject, as everything learned in the bosonic theory of the string can be applied and expanded to the case of the superstring. That is to say, I think it is worth spending the time working through Volume 1 before proceeding to Volume 2.

For some, I've seen complaints that this textbook (Vol. 1 and 2) are too dense for a reader learning the subject. Polchinski's approach, indeed, serves as a technical guide and there are pages where heavy background computation is less than obvious. So I understand the content matter may at times seem impenetrable. But I wholly recommend patient and thorough reading. If necessary, one could supplement Volume 1 and 2 with Green, Schwarz, and Witten (another excellent string textbook) or Becker, Becker, and Schwarz.