In these lectures, I will give a detailed introduction to the subject of holographic correlation functions and scattering amplitudes in anti de Sitter space. In particular, I will review the recent progress in computing tree-level four-point functions in diverse spacetime dimensions using methods inspired by the bootstrap philosophy. I will also discuss how we can compute loop corrections by leveraging CFT techniques. Along the way, I will point out various interesting properties and highlight the similarity between AdS and flat space amplitudes. Finally, I will conclude by briefly discussing some topics omitted in these lectures and listing a few interesting open problems.　

　　Lecture 1

　　Basics of CFT: embedding space formalism, OPE and conformal blocks [1].

　　Witten diagrams – everything you need to know.

　　The Mellin space formalism [2].

　　Lecture 2

　　Superconformal kinematics.

　　Bootstrap method I: the position space method [3].

　　Bootstrap method II: an algebraic approach for AdS5 [4].

　　Bootstrap method III: the maximally R-symmetry violating (MRV) method [5,6].

　　Lecture 3

　　Gluon Scattering in AdS and the MRV method [7].

　　Double copy in AdS [8].

　　Unitarity method and loop level amplitudes [9].

　　Open questions.

　　Recommended reading:

　　1.S. Rychkov, EPFL Lectures on Conformal Field Theory in D>=3 Dimensions, 1601.05000.

　　2.J. Penedones, Writing CFT correlation functions as AdS scattering amplitudes, JHEP 03 (2011) 025.

　　3.L. Rastelli, X. Zhou, How to Succeed at Holographic Correlators Without Really Trying, JHEP 04 (2018) 014.

　　4.L. Rastelli, X. Zhou, Mellin Amplitudes for AdS5 x S5, Phys.Rev.Lett. 118 (2017) 9, 091602.

　　5.L. F. Alday, X. Zhou, All Tree-Level Correlators for M-theory on AdS7 x S4, Phys.Rev.Lett. 125 (2020) 13, 131604.

　　6.L. F. Alday, X. Zhou, All Holographic Four-Point Functions in All Maximally Supersymmetric CFTs, Phys.Rev.X 11 (2021) 1, 011056.

　　7.L. F. Alday, C. Behan, P. Ferrero, X. Zhou, Gluon Scattering in AdS from CFT, JHEP 06 (2021) 020.

　　8.X. Zhou, Double Copy Relation in AdS space, Phys.Rev.Lett. 127 (2021) 14, 141601.

　　9.O. Aharony, L. F. Alday, A. Bissi, E. Perlmutter, Loops in AdS from Conformal Field Theory, JHEP 07 (2017) 036.