In Part 1 of this article1, we had introduced the idea of symmetry as a mapping that maps a given object onto itself, and we studied an important class of mappings, theisometries — the maps that leave distances unchanged. We showed that every isometry is either the identity, a rotation, a reflection, a translation or a glide reflection. In this part, we consider some further properties of isometries and make some remarks on the Erlangen programme of Felix Klein; then we classify the so-called frieze groups.