ATU is short for "Aarne–Thompson–Uther," and is a way of indexing folklore and fairytales
According to Stith Thompson, a tale type is "a traditional tale that has an independent existence. It may be told as a complete narrative and does not depend for its meaning on any other tale. It may indeed happen to be told with another tale, but the fact that it may be told alone attests its independence. It may consist of only one motif or of many"
The Aarne–Thompson–Uther Index is a helpful way to find specific tale types, as well as discover new ones. Tales are organized by certain key plot figures, such as "a modest request by the girl to her father (oftentimes asking for a rose), "the girl stays too long at home after granted permission by her capturer to visit for a shorter time," and " girl disenchants the beast with a kiss," which would designate the story as ATU 425C (Beauty and the Beast). There are overlaps in this categorizing system to be aware of.
The Aarne–Thompson–Uther Index is primarily Eurocentric, and does not include many fairy tales from other cultures, although it should be noted that in 2004 German folklorist Hans-Jörg Uther made changes to the index which expanded its reach. Additionally, the index does not account well for stories which contain tropes from mutliple ATUs, and as tales evolve through retellings, this becomes difficult.