Motif-Index of Folk-Literature by Stith Thompson.
There is an easy to use online version of the Thompson The Motif-Index
and there is also a scanned six volume e-book copy at the HathiTrust.
For an overview of this scheme please see this Wikipedia article.
Classification of Folk Tale Types
The Types of the Folktale: A Classification and Bibliography / Stith Thompson
This is earlier version of the classification. The types from this classification are prefixed with AT
(for Aarne who originally devised it and for Thompson who translated and enlarged it.)
The classification was later revised and type numbers based on that revised classification are prefixed with ATU. (For Aarne, Thompson, and Uther).
See this Wikipedia article for an overview.
The complete ATU classification in available only in print in a book called:
|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. and are volumes no. 284, 285, and 286.
These books are NOT ONLINE as far as can determine. You will have to locate them in your local library.
While incomplete, a GREAT PORTION of the AT and ATU classification schemes can be found here.