The Department of Physics
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References
These are the three main references that I suggest:
H. Nastase, Introduction to the ADS/CFT Correspondence , Cambridge University Press 2015.
This is a dedicated textbook, which starts from the very basics and explains the basis of GR, QFT, string theory and everything else needed as a background (although some of the background material is stripped down to the essential). (it may not be easy to find though)
A. Zaffaroni, Introduction to the AdS/CFT correspondence,
Lecture notes for various courses given around 2010. Easy to follow, does not use string theory until half-way through the course, and when it does it makes the effort of explaining the basic ingredients.
Available at http://virgilio.mib.infn.it/~zaffaron/lectures.html
J. Penedones, Tasi Lectures on AdS/CFT. Again no strings required. CFT part very well developed.
Available at https://arxiv.org/abs/1608.04948
There are plenty of other reviews and lecture notes on AdS/CFT. A few of them are:
MAGOO, The classic review paper on the subject, written by the founding fathers. Not easy but contains a thorough discussion of stringy stuff, susy and calculations of the first checks of the correspondence.
Available at https://arxiv.org/abs/hep-th/9905111
Matteo Baggioli, A practical mini-course on applied holography,
Lots of developed explicit calculations and tricks.
Avaiable at https://arxiv.org/abs/1908.02667
Francesco Benini, lectures given at SISSA.
Avaiable at https://www.sissa.it/tpp/phdsection/descriptioncourse.php?ID=16
For background material on QFT, gauge theories and General Relativity, in case you want a crash course or a review, I suggest the excellent lectures by David Tong on both subjects, which can be found here:
http://www.damtp.cam.ac.uk/user/tong/teaching.html
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