Choose an App

There are many more than these, this is just a small list of what i've seen.

After installing, open the app and enter https://books.rosebromedia.org as your server address, then sign in with your usual credentials.

Android

ABS Official App
Google Play

What I personally use.
ABSorb
Google Play

New app, can't vouch but people like it.

Apple - Haven't used these but they are mentioned often.

Plappa
Website
Audiobooth
App Store
Official IS IN TESTING
App Store

Has been in testflight for awhile. No clue when it will be available

Other

Web Browser No install needed
Open

Just another link to the website.
Server address https://books.rosebromedia.org

Enter this when the app asks for your AudioBookShelf server URL.