There is a world’s oldest library.
Now part of a university, it is the Al-Qarawiyyin library in Morocco.
Founded in 859CE by a lady called Fatima al-Fehri, it contains ancient and mediaeval manuscripts as well as books.
It has recently undergone a major restoration with special moisture management systems installed to protect the precious manuscripts.
Some libraries have birthdays.
Apparently the Library of Congress celebrated its birthday recently. On April 24th 1800 then president John Adams parented the library by approving the necessary expenditure. I doubt if it got a cake with 217 candles on it, but its anniversary was marked in several places, including a collection of trivia from Bookriot.
Some libraries use unique classification systems.
The Levinski Garden Library shelves its books according to the emotions they raise in their readers. Each reader is asked to describe the book’s effect: sad, happy, boring etc. The emotions are colour coded and the returned book gets a piece of coloured tape and is then shelved according to the most recent one.