Here are 4 screenshots from the app taken on my Galaxy Nexus. Standard warning: details might change, but I don't think they will change by much.
1: Books sorted by title. This is the initial view when starting the app.
2: Book sorted by author
3: Transferring from calibre. There are two progress bars, one for where the app is in the series of books, the other for the book being transferred. The author is visible in the book progress bar because that book's title contains the author's name.
4: Grouping. The display behind the menu is grouped by author. If you tap on a letter line you will see a list of authors beginning with that letter. Tapping on an author takes you to books. Tapping "User Categories" takes you to the list of sony-style collections. This item does not display if no collections are defined, which is the default. The two items at the end are lookup keys for custom columns I chose to use for grouping.