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Well, when you say " le livre des Ratier", it suggests that It belong to many " Ratier"

When you say " le livre de Ratier", It means that the book belong to one person.

" le livre de ratier" would mean the same thing.

"Des" is used in front of a plural noun.

"À" and "De" can be used in more than one case.

Here's a link.

http://www.francaisfacile.com/exercices/exercice-f...

This website is one of the best I know to learn French.

If the book is written _by_ somebody called "Ratier" it's "le livre de Ratier".

If the book is written _about_ somebody called "Ratier" it's "le livre sur Ratier".

If the book is physically located in a _place_ called "Ratier" it's "le livre à Ratier".

If the book is written about mousers (cats who are good at catching mice), it's "le livre des ratiers".

Honestly, I don't see any other possibilities.