  We examine the notion of symmetry in quantum field theory from a fundamental
representation theoretic point of view. This leads us to a generalization
expressed in terms of quantum groups and braided categories. It also unifies
the conventional concept of symmetry with that of exchange statistics and the
spin-statistics relation. We show how this quantum group symmetry is
reconstructed from the traditional (super) group symmetry, statistics and
spin-statistics relation.
  The old question of extending the Poincare group to unify external and
internal symmetries (solved by supersymmetry) is reexamined in the new
framework. The reason why we should allow supergroups in this case becomes
completely transparent. However, the true symmetries are not expressed by
groups or supergroups here but by ordinary (not super) quantum groups. We show
in this generalized framework that supersymmetry remains the most general
unification of internal and space-time symmetries provided that all particles
are either bosons or fermions.
  Finally, we demonstrate with some examples how quantum geometry provides a
natural setting for the construction of super-extensions, super-spaces,
super-derivatives etc.
