  We give a pedagogical review of how concepts from quantum information theory
build up the gravitational side of the AdS/CFT correspondence. The review is
self-contained in that it only presupposes knowledge of quantum mechanics and
general relativity; other tools--including holographic duality itself--are
introduced in the text. We have aimed to give researchers interested in
entering this field a working knowledge sufficient for initiating original
projects.
  The review begins with the laws of black hole thermodynamics, which form the
basis of this subject, then introduces the Ryu-Takayanagi proposal, the JLMS
relation, and subregion duality. We discuss tensor networks as a visualization
tool and analyze various network architectures in detail. Next, several modern
concepts and techniques are discussed: Renyi entropies and the replica trick,
differential entropy and kinematic space, modular Berry phases, modular minimal
entropy, entanglement wedge cross sections, bit threads, and others. We discuss
the extent to which bulk geometries are fixed by boundary entanglement
entropies, and analyze the relations such as the monogamy of mutual
information, which boundary entanglement entropies must obey if a state has a
semiclassical bulk dual. We close with a discussion of black holes, including
holographic complexity, firewalls and the black hole information paradox,
islands, and replica wormholes.
