  Adjoint methods can speed up stellarator optimisation by providing gradient
information more efficiently compared to finite-difference evaluations. Adjoint
methods are herein applied to vacuum magnetic fields, with objective functions
targeting quasisymmetry and a rotational transform value on a surface. To
measure quasisymmetry, a novel way of evaluating approximate flux coordinates
on a single flux surface without the assumption of a neighbourhood of flux
surfaces is proposed. The shape gradients obtained from the adjoint formalism
are evaluated numerically and verified against finite-difference evaluations.
