  We are concerned with orderable groups and particularly those with orderings
invariant not only under multiplication, but also under a given automorphism or
family of automorphisms. Several applications to topology are given: we prove
that the fundamental groups of hyperbolic nonorientable surfaces, and the
groups of certain fibred knots are bi-orderable. Moreover, we show that the
pure braid groups associated with hyperbolic nonorientable surfaces are
left-orderable.
