This course will provide a modern point of view on the wide world of large $N$ conformal field theory (CFT) in diverse spacetime dimensions, placed in the context of the conformal bootstrap and the AdS/CFT Correspondence. Some questions we will tackle: What is a “Holographic CFT”? — When does a CFT give rise to an equivalent, emergent simple gravity description? — What is the conformal bootstrap, and how is it used to constrain and classify the space of consistent large $N$ CFTs and theories of quantum gravity? — Is string theory the only choice? How can we detect strings and extra dimensions from properties of field theories? — What precise predictions does quantum gravity seem to make about the space of strongly coupled CFTs? Provisional lecture plan: Lectures I-II: Introducing CFTs and their data, large $N$ conformal bootstrap, AdS/CFT, and the notion of “Holographic CFT” Lecture III: Correlation functions and holography Lecture IV: Bootstrapping the space of Holographic CFTs Lecture V: Special focus: Two-dimensional CFTs and AdS$_3$ gravity Course website: https://courses.ipht.fr/?q=en/node/310 Videoconference and in person in Salle Itzykson, IPhT Livestream on youtube.com/IPhT-TV: no subscription required