  The nuclear symmetry energy characterizes the variation of the binding energy
as the neutron to proton ratio of a nuclear system is varied. This is one of
the most important features of nuclear physics in general, since it is just
related to the two component nature of the nuclear systems. As such it is one
of the most relevant physical parameters that affect the physics of many
phenomena and nuclear processes. This review paper presents a survey of the
role and relevance of the nuclear symmetry energy in different fields of
research and of the accuracy of its determination from the phenomenology and
from the microscopic many-body theory. In recent years, a great interest was
devoted not only to the Nuclear Matter symmetry energy at saturation density
but also to its whole density dependence, which is an essential ingredient for
our understanding of many phenomena. We analyze the nuclear symmetry energy in
different realms of nuclear physics and astrophysics. In particular we consider
the nuclear symmetry energy in relation to nuclear structure, astrophysics of
Neutron Stars and supernovae, and heavy ion collision experiments, trying to
elucidate the connections of these different fields on the basis of the
symmetry energy peculiarities. The interplay between experimental and
observational data and theoretical developments is stressed. The expected
future developments and improvements are schematically addressed, together with
most demanded experimental and theoretical advances for the next few years.
