  Entanglement entropies have revealed, in the last years, to be a powerful
tool to extract information about the physics of condensed-matter systems. In
the first part of this thesis, we show how to extract essential details about
the quasi-long-range order of a one-dimensional critical systems by means of
entanglement entropies. In the second part we show how to derive analytically
the scaling of such quantities for critical systems, whose low-energy physics
is described by a conformal field theory, in presence of general open boundary
conditions that preserve the conformal invariance.
