Welcome to MR, Suziki1 !
Our MR Wiki has a page called
Sony Reader Troubleshooting Guide. Click on "Borrowing library books" to find information about reading library books on your Reader.
When you install ADE you must use the SAME log in and password that you used for Sony Reader Library in order for the books to be opened.
Also, please take note of this information in that section: "You can borrow epub and pdf books from your library, but be careful to never have both epub and pdf library books on your reader at the same time, as there is a conflict and you will not be able to access them."
I hope this helps and please let us know what happens.