The physical world is marked by the phenomenon of spontaneous broken symmetry
(SBS) i.e. where the state of a system is assymmetric with respect to the
symmetry principles that govern its dynamics. For material systems this is not
surprising since more often than not energetic considerations dictate that the
ground state or low lying excited states of many body system become ordered
i.e. a collective variable, such as magnetization or the Fourier transform of
the density of a solid, picks up expectation values which otherwise would
vanish by virtue of the dynamical symmetry(isotropy or translational symmetry
in the aforementioned examples). More surprising was the discovery of the role
of SBS in describing the vacuum or low lyng excitations of a quantum field
theory. First came spontaneously broken chiral symmetry which was then applied
to soft pion physics. When combined with current algebra, this field dominated
particle physics in the 60's. Then came the application of the notion of SBS to
situations where the symmetry is locally implemented by gauge fields. In that
case the concept of order becomes more subtle. This development lead the way to
electroweak unification and it remains one of the principal tools of the
theorist in the quest for physics beyond the standard model. This brief review
is intended to span the history of SBS with emphasis on conceptual rather than
quantitative content. It is a written version of lectures of R.Brout on the
``Paleolithic Age'' and on ``Modern Times'' by F.Englert, i.e. respectively
without and with gauge fields.Comment: LaTeX file 28 pages, 9 figures. Presented at the 2001 Corfu Summer
Institute on Elementary Particle Physic
