Wow. That's a pile of books.
According to the Republic of Ireland's Copyright and Related Rights Act, 2000, the Library is entitled, along with the National Library of Ireland and the libraries of the National University of Ireland, the University of Limerick, and Dublin City University, to receive a copy of all works published in the Republic of Ireland. Also, as a result of the British Legal Deposit Libraries Act 2003, which continues a more ancient right dating from 1801, the Library is entitled, along with the British Library, the Bodleian Library at Oxford, Cambridge University Library, the National Library of Wales and the National Library of Scotland, to receive a copy on request of all works published in the United Kingdom.
It's a wonderful library, and you can see The Book of Kells.
The Book of Kells (Digitalcollection, Trinity College Dublin)+-- Book of Kells (Wikipedia)