The Aarne-Thompson-Uther Classification of Folk Tales (ATU) is a catalog of international tale types. It is an expansion of the system first developed by Aarne (1910) for European tales and later expanded by Thompson (1928, 1961) to include more tales from Europe as well as tales from India.
The classification scheme used to be online, but the website it was on has been taken down.
The broad outline of the classification is still available, but the links to individual tales no long work.
The only place to find the complete ATU Classification in a the print publication.
The types of international folktales : a classification and bibliography, based on the system of Antti Aarne and Stith Thompson / by Hans-Jörg Uther. Published Helsinki : Suomalainen Tiedeakatemia, Academia Scientiarum Fennica, 2004.
This was published in a series of books called FF communications. The classification is in volumes no. 284, 285, and 286.
These books are not online, You will have to locate them in a library.
You can, however, find ATU numbers for most of Grimm's Fairy Tales on D.L. Ashliman's site.
The ATU classification replaced the AT classification by combining some of the types. The older AT classification is on site called the Golden Scales, Except for Norwegian folk tales, this site only lists the AT numbers, it does not link to the folk tale.
The Classification of Folk Tales should not to be confused with the Stith Thompson Motif-Index of Folk Literature. The ATU catalog is a classification of the whole plot of a story into seven broad categories: Animal Tales, Tales of Magic, Religious Tales, Realistic Tales, Tales of the Stupid Ogre (Giant, Devil), Anecdotes and Jokes, and Formula Tales. The classification uses numbers 1-2000. References to the older Aarne-Thompson classification have the AT prefix. Those the Aarne-Thompson-Uther classification use the ATU prefix. The AT numbers were subsumed within the ATU classification.
The scheme of the Stith Thompson Motif-Index of Folk-Literature is is available online.
The physical volumes are available in Ellis Reference GR 67 .T52 as well as online at the HathiTrust. There are six volumes:
The online scheme is probably easier to use. The Thompson Motif Index is in the middle of the page. Broad categories are at the top of the page and specific motifs are below. The MOTIFS ARE IN RED.
An entry will look like this:
A 753. Moon as person
A753.1 Moon as wooer
A753.1.1 Moon abducts woman. Eskimo (Kodiak): Golder JAFL XVI 29.
A753.1.1 is an Eskimo folk tale and is mentioned by an author name Golder, in volume 16 (Roman numeral XVI) on page 29 of a publication abbreviated JAFL.
To locate this online, use the tabs on the left hand side of this page. For example, if you search the H - M tab for JAFL you will find *JAFL = Journal of American Folk-Lore. Boston, etc., 1888 ff.. Entries which are available in the HathiTrust or the Internet Archive are linked. Once connected to the text, use the page number given in the entry to navigate to the start page of the tale.
The most useful volume at the Hathitrust is Volume Six, the Index. For example, you could use it to find folk-tales that have a LION in them. Another way to look up LION would be to use Story Search. It is an online database of "Motifs" from the Stith Thompson Motif Index of Folk-Literature. It can only search single words, but it might be useful in finding a motif number for a story. You can then search the Motif-Index to find the story.