In addition to the published primary literature (which one needs to identify mayflies to species), the books listed below are useful to have. Some are old, and some are really old, but the truth of the matter is, we still use these resources. The reason for this are as follows: 1) in some cases there is no modern equivalent (e.g, the key to adult Baetis in Traver 1935); 2) there is information that has not been published anywhere else (e.g., Day’s table of larval characters to the Paraleptophlebia in his Aquatic Insects of California); or 3) the figures are just very well done (e.g., Edmunds et al. 1976).
Unfortunately not all of the books listed are in print, but one can track them down online. The actual books are available for purchase at various sites, but look around as some of the pricing is ridiculous. The Digital Public Library of America and the Biodiversity Heritage Library have links to some out of print texts.
An Introduction to the Aquatic Insects of North America. 2008. Merrit and Cummins, eds. This is required if you are not familiar with the families and genera. It is the most up-to date and complete keys to Families and Genera (it does not do species level identification). But since the latest version was published in 2008, some of the names are out of date. Note: This book did come with a cd with images, but unfortunately it won’t run on modern computers (the downside of digital media is the continuing changes in format.)
The Biology of Mayflies. Needham, Traver, Hsu. 1935. This is nice to have, but not a necessity if you are only interested in larvae. For adults, however, for certain groups (Baetis adults), it is the only key available. Just from a historical perspective, it is an important book.
A pdf can be found here: https://catalog.hathitrust.org/Record/001500213
Aquatic Insects of California. Day. 1956. Also not a necessity but I have found it helpful in many cases. First it is focused on California fauna, making it easier to use than The Biology of Mayflies. It does provide some information not published elsewhere.
A pdf can be found here: https://www.biodiversitylibrary.org/bibliography/61952#/summary
Mayflies of North and Central America. 1976. Edmunds, Jensen, and Berner. This book is less useful for the California fauna, but it does have many great figures drawn by Steve Jensen. Also, this book does include a ton of biology.
The mayflies of Idaho (Ephemeroptera). Jensen, S. L. 1966. Unpublished Masters Thesis. Univ. Utah, Salt Lake City. 367pp. This is a Master’s thesis that still has use. I have not had any luck finding it online, unfortunately. Jensen’s thesis includes many excellent figures and keys that can help with some identification. Given the focus is Idaho, it does have limited use, but I do use it as a supplement to the published literature (primarily larval Paralepthophlebia).