Anyway I thought I would look at what could be in a fairytale or other fictional library. Part of the role of any fiction author is to produce well rounded characters. They must seem real to readers so they willingly suspend disbelief for the duration of that story/novel (and sometimes at least poems too. I've read some great character based work). So to bring about that well rounded character, any author is going to have to know what makes that character tick to be able to write about/for them convincingly.
All writers love books and reading (indeed you can't write without reading well. How else will you know what you want to write? Inspiration has to come from somewhere. And all writers build on what has gone before so you have to know what has gone before, at least in the genre in which you want to write). So characters then will have their own tastes, one of which will be in literature.
What books do your characters read? Is literacy high in the fictional world you've created? What stories and legends are the foundation of your setting that every one of your characters would know about (and probably be influenced by)?
A fairytale library, for me, would contain the classic tales but also fables, legends and myths from not just the world in which it is set but other worlds that universe knows about. Libraries collect after all. So who would run your fictional libraries? Does everyone have access to them? Can everyone read?