Volume 1: An Introduction to the Bosonic String
Volume 2: Superstring Theory and Beyond
by Joe Polchinski (two volumes, CUP, 1998, errata)
This book addresses the discoveries of the superstring revolutions of the early to mid 1990s, which mark the beginnings of modern string theory. Volume 1 quantises the bosonic string and uses this setting to introduce T-duality and D-branes without the complications of fermions. The first three chapters of volume 2 introduce superstrings, but quickly move beyond. The rest of the second book provides an introduction to nearly all modern string topics pre-dating the AdS/CFT duality. In particular, it includes D-branes, Orbifolds, Black Hole Entropy, and Mirror symmetry.
Some of the errata were corrected in the reprinting in 2000.
Volume 1: Introduction
Volume 2: Loop Amplitudes, Anomalies and Phenomenology
by Michael Green, John Schwarz and Edward Witten (two volumes, CUP, 1988)
Volume 1 is the first of a classic two-volume string text by founders in the field. Though there are now many more modern texts, it containing many details that more recent texts must skim through to discuss modern topics. Volume 1 is concerned mainly with the free string, though it treats both bosonic and supersymmetric versions. Volume 2 addresses the details of loop calculations, but also discusses low-energy effective theories (in particular, supergravity) and compactifications (especially on Calabi-Yau manifolds).
String Theory and M-Theory
by Katrin Becker, Melanie Becker and John Schwarz (CUP, 2006)
A First Course in String Theory
by Barton Zwiebach, (CUP, 2003)
This book is intended for the advanced undergraduate or beginning graduate level. No familiarity with quantum field theory is assumed (although Zwiebach does assume a working knowledge of quantum mechanics). It focuses on the study of single strings and their interactions, which can be understood in some detail. Of necessity, however, it is impossible to address many advanced topics.
Supersymmetry and String Theory: Beyond the Standard Model
by Michael Dine (CUP, 2007)
Gravity and Strings