  In this paper, we derive the first order approximate symmetries for the Harry
Dym equation by the method of approximate transformation groups proposed by
Baikov, Gaszizov and Ibragimov. Moreover, we investigate the structure of the
Lie algebra of symmetries of the perturbed Harry Dym equation. We compute the
one-dimensional optimal system of subalgebras as well as point out some
approximately differential invariants with respect to the generators of Lie
algebra and optimal system.
