liber

Liber, libri is second declension masculine, and the -e- of the nominative drops out everywhere else: libri, libro, librum, libros, not liberi. That single detail settles most of the confusion around the word.

The confusion is real, because three different words share the shape liber. This noun, "book"; the adjective liber, libera, liberum, "free", whose stem keeps the e, so its plural liberi means "free men" and, by a very Roman leap, "children"; and Liber, the god identified with Bacchus. Genitive libri is "of the book", genitive liberi is nothing of the sort. The original sense here is the inner bark of a tree, which is what people wrote on before papyrus was cheap. Family: libellus, librarius, bibliotheca borrowed from Greek. English library, libel (a little book, then a defamatory one); French livre, Spanish libro, Italian libro.