Significant writers of fairy tales

The modern definition of a fairy tale is that it is simple and anonymous and written by a single identifiable author- though how would that mean it's anonymous? Anyway, many of the common fairy tales we see today are written by (well, attributed to) just a few authors. For example:

• The 18th century German Grimm Brothers (Jacob and Wilhelm) appear to be responsible for a number of famous fairy tales, including Hansel and Gretel, Rapunzel, Cinderella and Sleeping Beauty. 

• Hans Christian Anderson was a 19th century Danish poet who wrote such tales as The Little Mermaid, Thumbelina and The Ugly Duckling.

• There was also a Russian folklorist who didn't specifically write fairy tales, but collected over 600 Russian folktales such as the Fox and the Geese and the Swan-Geese.

Though a number of fairy tales can be pinned down to be written by one author, many remain anonymous (like the Arabian Nights collection) because they have grown out of an oral tradition. Even when tales are attributed to specific authors this does not guarantee sole authorship as what they write down is often just one version of a story which may have been around for generations.