Abstract
These notes, based on lectures given at various schools over the last few
years, aim to provide an introduction to entanglement entropies in quantum
field theories, including holographic ones. We explore basic properties and
simple examples of entanglement entropies, mostly in two dimensions, with an
emphasis on physical rather than formal aspects of the subject. In the
holographic case, the focus is on how the Ryu-Takayanagi formula geometrically
realizes general features of field-theory entanglement, while revealing special
properties of holographic theories. In order to make the notes somewhat
self-contained for readers whose background is in high-energy theory, a brief
introduction to the relevant aspects of quantum information theory is included.