Various is the correct author for any book with multiple unknown authors, and is acceptable for books with multiple known authors, especially if not all are known or the list is very long (over 50).
If an editor is known, however, Various is not necessary. List the name of the editor as the primary author (with role "editor"). Contributing authors' names follow it.
Note: WorldCat is an excellent resource for finding author information and contents of anthologies.
This is an anthology of short stories or fables. The collection is quite diffuse with examples from Europe, Asia, Native Americans, etc. There is even the odd Scottish and Irish story. This book was published in 1958, so many of the stories are rather old, and probably oral classics before they were codified. It is unfortunate that the editor(s) did not include a description or history of each work. It would make things more interesting.
The stories are magical and fantastic. Most of them have a moral counterpart. A few of them are just strange and bizarre. Most are clever and very original. Not all of them are a beautiful princess battling an evil stepmother (although a common theme) seeking a handsome prince. More than one prince is actually the poorest of the poor with the hero's spirit making them a prince. Most of the stories do support the basic idea that a girl must, must find a husband. Most of them also emphasize luck brings fortune instead of hard work and cleverness. So, the stereotypical children's tales are alive and well. Only the stories by Grimm have some blood.
Overall, they provide a fascinating glimpse into some original storylines. The characters are usually sympathetic to the readers. They are short and entertaining. Good reading.