Free. Everyone gets this.
Shelves are named groups of books, like “Book club”, “Stoics” or “Summer reading”. A book can sit on as many shelves as you like.

Click a shelf’s name. The Library shows only the books on it. Click All books to see everything again.
When you’re looking at one shelf, drag the covers into the order you like. Reading Vault remembers it. This is great for a series.
Look at the shelf, then press ⋯ next to its name. Pick Rename shelf or Delete shelf.
Deleting a shelf never deletes a book. The books just stop being on that shelf.