The following solutions are given in two cases:

One,

If seven books are the same seven books,

First, give each library 1 book to ensure that each library has at least one book, and then the remaining four books can be distributed at will;

Situation discussion:

There are three ways to give all four books to a library;

② Distribute four books to two libraries and choose two books from three libraries. There are three methods: c (3,2) = 3; The two selected databases are divided into four books, and there are three methods: (1, 3) (2,2) (3,1) * *; Then * * * has 3×3 = 9 methods;

③ Distribute four books to three libraries in three ways: (1, 1, 2) (1, 2, 1) (2, 1,1) * *;