  Entanglement entropy plays a variety of roles in quantum field theory,
including the connections between quantum states and gravitation through the
holographic principle. This article provides a review of entanglement entropy
from a mixed viewpoint of field theory and holography. A set of basic methods
for the computation is developed and illustrated with simple examples such as
free theories and conformal field theories. The structures of the ultraviolet
divergences and the universal parts are determined and compared with the
holographic descriptions of entanglement entropy. The utility of quantum
inequalities of entanglement are discussed and shown to derive the C-theorem
that constrains renormalization group flows of quantum field theories in
diverse dimensions.
