1. Motivation: The Black Hole Guide to the Quantum Theories of Gravity Quantum theory of General Relativity and its breakdown Transplanckian black hole dominance and the non-Wilsonian character of gravity Black holes in AdS_d from Conformal field theory in d-1 (Non-AdS holography?) 2. The gravitational path integral Black hole thermodynamics: general aspects and Euclidean formalism The gravitational path integral Entropy and thermodynamics from gravitational action 3. Basics of AdS/CFT holography Geometry of AdS Fields in AdS / Operators in CFT Divergences and holographic renormalization The holographic stress tensor 4. Thermal states in AdS/CFT Phases of AdS black holes. Hawking-Page transition The eternal black hole and the thermofield double 5. AdS/CFT from strings and D-branes Gauge theory from open strings, gravity from closed strings D-branes as gauge theories and as black holes Decoupling limit and AdS/CFT The D1D5 CFT 6. Low-dimensional models AdS3/CFT2. The BTZ black hole and its CFT dual AdS2, JT gravity and the Schwarzian action 7. Holography and entanglement Basics of entanglement Holographic entanglement entropy: the Ryu-Takayanagi formula Holographic entanglement in vacuum and in thermal states Entanglement wedges and bulk reconstruction
