Conformal Field Theory intro.

I highly recommend Ginsparg as an introductory set of notes:
http://arxiv.org/abs/hep-th/9108028

As a good second source, which you should keep aside (but is a little less detailed), try Schellekens notes:
http://www.nikhef.nl/~t58/lectures.html

In the end there is only one real Tome on conformal field theory, which is the book by Di Francesco, Mathieu and Senechal (title: Conformal Field Theory). But that will take you at least a whole year to read back-to-back. Do note that this book is about CFT - not about its applications (for instance, it hardly involves supersymmetry).

In the context of String theory you should also look for Polchinski, String Theory Vol 1.

 

xepma makes a point however : it depends whether you want to study conformal field theory by itself, or if you have a specific application for it. There are numerous books on it in condensed matter field theory for instance.

A shorter review is in RMP Vol 34 num 3 (Jul 1962) page 442

 

For condensed matter, I have "Introduction to conformal invariance and its applications to critical phenomena" by Christe and Henkel (CUP 1993) (but as you know, I am no condensed matter aficionado, so there may be better references around)

Also, there is "Applied conformal field theory" by Ginsparg (Les Houches 1989)