The largest library in the world today by collection size is the Library of Congress. The Library was established on this day in 1800 when then President John Adams signed an act of Congress that moved the United States seat of government from Philadelphia to Washington D.C. Part of that bill approved the establishment of the library and devoted $5000 toward the purchase of books. A history of the Library on its own web site informs us that altogether the original collection had 740 books and 3 maps.

And from there it's been all uphill - which also brings its own share of problems. That same LOC source tells us that today the Library houses over 100 million items. A Washington Post article from 2007 reports that according to a survey submitted to Congress:

About one-sixth of the books, monographs and bound periodicals at the Library of Congress weren't where they were supposed to be because of flaws in the systems for shelving and retrieving materials