How many parts are there of movie Lord of the Rings?

there are three books that are published separately: the fellowship of the ring, the two towers and the return of the king, but within each one is two "books." the fellowship is "books" 1 and 2 and the two towers starts with "book" 3. in each book are also chapters and stuff. there is also The Hobbit which is part of the same history surrounding the ring, but not part of the lord of the rings