This is Ireland's oldest university, founded in 1592 by Queen Elizabeth I on the site of a monastery. Jonathan Swift, Oscar Wilde, Samuel Beckett, Bram Stoker, Wolfe Tone are some past students.
You don't have to pay to enter the college grounds and experience the quiet tranquility of the cobbled courtyards and pristine lawns; however it's well worth the admission to visit the 18th century Long Room, which houses over 200,000 books, and see the famous Book of Kells, a 9th century illuminated manuscript.
There's also The Dublin Experience, a multi-media presentation of Dublin history from Viking times to the present day.
Alternatively, you can pay for a guided walking tour of the
grounds, which is good value since it also includes admission
to the Book of Kells / Long Room.