Self study work

Library of Congress, Washington D.C., USA: 1.9 million visitors per year
The Library of Congress is not only the oldest federal cultural institution in the United States (it was founded in 1800), but is also the largest library in the country and is among the largest in the world, if not the largest. According to its website, the library hosted “nearly 1.9 million onsite visitors” in 2017—to peruse its 167,000,738 items on about 838 miles of bookshelves.

British Library, London, UK: 1.5 million visitors per year
The British Library rivals the Library of Congress in terms of the size of their holdings, with over 150 million items, many of them unique. According to their annual report, the British Library welcomed “almost 1.5 million” visitors in the 2016-2017 fiscal year, this figure representing “a small but disappointing reduction in our overall visitor numbers.” (In response they will be “making improvements to [their] Treasures Gallery,” which seems like it will work.)

Royal Danish Library, Copenhagen, Denmark: 1.44 million visitors per year
Okay, this one’s a little wonky, because the most recent official information I could find is from 2014, when 1.44 million people visited the Royal Library in Copenhagen. But in January of 2017, Denmark’s State and University Library and the Royal Library merged into the Royal Danish Library—a move I can only imagine has upped the visitor level, when taken as a whole. Still, as ever, I’m working with what I’ve got here.
Berlin State Library, Berlin, Germany: 1.4 million visitors per year
According to this website and Wikipedia, 1.4 million people visited the Berlin State Library (Staatsbibliothek zu Berlin) in 2009. I can’t confirm this, because I don’t read German, but I did find what appears to be a more recently updated stats page for the library—also in German, of course. If you can read it, update me.

Russian State Library, Moscow, Russia: 1.17 million visitors per year
I ran into another translation issue here, because the intel on Moscow’s Russian State Library is—shockingly—in Russian. But according to this website, the Russian State Library maintains about 44.4 million items and fields 1.17 million annual visitors.
Bibliothèque nationale de France, Paris, France: 1.15 million visitors per year
The national library of France, which boasts a collection of 15 million books and other items, reported 1,150,000 visits across its four Parisian branches in 2016. It’s also a pretty common (and gorgeous) tourist destination.
National Library of Russia, St. Petersburg, Russia: 1 million visitors per year
According to their website, in 2011, 966,000 people (I am rounding up) visited the reading rooms of the National Library of Russia, which has a collection of 35,718,000 items—though unlike some others on that list, that number was on a downward trajectory. It’s not clear what has happened in the last few years, but even if there are only (only!) a million visitors per annum, it’s worth mentioning here.
Trinity College Library, Dublin, Ireland: 1 million visitors per year
According to their annual report, the Trinity College Library—the largest library in Ireland—welcomed over 964,000 visitors in 2017, which again, I am rounding up to a million. Many of those came to see the Book of Kells—a gorgeous 9th century illuminated manuscript that is among Ireland’s greatest sights—and the famous Long Room, which also ranks pretty highly as far as sights go, in my opinion.