  The discovery of quasicrystals has changed our view of some of the most basic
notions related to the condensed state of matter. Before the age of
quasicrystals, it was believed that crystals break the continuous translation
and rotation symmetries of the liquid-phase into a discrete lattice of
translations, and a finite group of rotations. Quasicrystals, on the other
hand, possess no such symmetries-there are no translations, nor, in general,
are there any rotations, leaving them invariant. Does this imply that no
symmetry is left, or that the meaning of symmetry should be revised? We review
this and other questions related to the liquid-to-crystal symmetry-breaking
transition using the notion of indistinguishability. We characterize the
order-parameter space, describe the different elementary excitations, phonons
and phasons, and discuss the nature of dislocations-keeping in mind that we are
now living in the age of quasicrystals.
