  The dynamics of symmetry breaking during out of equilibrium phase transitions
is a topic of great importance in many disciplines, from condensed matter to
particle physics and early Universe cosmology with definite experimental
impact. In these notes we provide a summary of the relevant aspects of the
dynamics of symmetry breaking in many different fields with emphasis on the
experimental realizations. In condensed matter we address the dynamics of phase
ordering, the emergence of condensates, coarsening and dynamical scaling. In
QCD the possibility of disoriented chiral condensates of pions emerging during
a strongly out of equilibrium phase transition is discussed. We elaborate on
the dynamics of phase ordering in phase transitions in the Early Universe, in
particular the emergence of condensates and scaling in FRW cosmologies. We
mention some experimental efforts in different fields that study this wide
ranging phenomena and offer a quantitative theoretical description both at the
phenomenological level in condensed matter, introducing the scaling hypothesis
as well as at a microscopic level in quantum field theories. The emergence of
semiclassical condensates and a dynamical length scale is shown in detail, in
quantum field theory this length scale is constrained by causality. The large N
limit provides a natural bridge to compare the solutions in different settings
and to establish similarities and differences.
