  The AdS/CFT correspondence provides quantum theories of gravity in which
spacetime and gravitational physics emerge from ordinary non-gravitational
quantum systems with many degrees of freedom. Recent work in this context has
uncovered fascinating connections between quantum information theory and
quantum gravity, suggesting that spacetime geometry is directly related to the
entanglement structure of the underlying quantum mechanical degrees of freedom
and that aspects of spacetime dynamics (gravitation) can be understood from
basic quantum information theoretic constraints. In these notes, we provide an
elementary introduction to these developments, suitable for readers with some
background in general relativity and quantum field theory. The notes are based
on lectures given at the CERN Spring School 2014, the Jerusalem Winter School
2014, the TASI Summer School 2015, and the Trieste Spring School 2015.
