If you've read Possession, you will recognise the first two stories, "The Glass Coffin" and "Gode's Story", from there. You will also understand the different meanings they have in these two contexts: whereas in Possession they are framed by the main story and signal female freedom and childbirth for the 19th century female protagonist, Christabel LaMotte, in this volume they stand alone, so you can further appreciate their postmodern writing and the way Byatt rewrites an old form into a quite modern one. You read the stories through a different lens, which makes their meaning quite different.
The story that gives the name to the book is a pure joy to read. In it, you find a female narratologist, Gillian Perholt (wink to the famous French fairy-tale writer Perrault), who is going through a midlife crisis sparkled by the fact that her husband has left her for a much younger woman. However,from storyteller in a conference in Turkey she will become the heroine of an Arabian fairy tale of her own, complete with a djinn (genie) in a nightingale's eye (a Venetian glass bottle)that will grant her three wishes: first she wishes for her body to be like it was when she last really liked it; then she wishes the genie would love her; and finally... you'll have to read it to find out. Both ancient and modern, spiced with references from A Thousand and One Nights and flavoured with Byatt's own recurrent leit-motifs such as the (apparent) dichotomy between ice and fire or the symbolic use of colours, this tale captures the texture of the Arabian story while creating a whole new world. Brilliant.
If you like traditional fairy stories, you will like these ones, although they may surprise you. If you like metamorphoseing old into new without losing the grip of neither world, you will positively delight in these stories. So...just read them!