While some of Ulysses was serialized in 1918, the true first edition wasn't published until 1922 by Sylvia Beach at her infamous Left Bank bookstore, Shakespeare and Company. The first printing comprised 1000 copies. 150 copies were printed on a large format, cheapish paper, 750 were numbered and used hearty linen, but the real rarity was the 100 copy Primary Edition signed by Joyce. This copy, number 45 of the 100, is one of among four copies -- of that prestigious batch -- that had yet to be accounted for, leaving three copies still lost. So, check your bookshelves!
Based on its earlier serialization, Ulysses was banned for obscenity here in the United States prior to the first edition being published in France. A pirated printing, now known as the Roth Edition (currently fetches $15,000), didn't appear in the U.S. until 1929, and it wasn't until 1934, after Random House won the historic United States vs. One Book Called Ulysses, that the "proper" American First Edition was published.
Ulysses #45 was actually bought illegally in New York City at the Sunwise Turn Bookstore, which closed its doors some six years before the ban on the book was lifted. The original owner passed the book down through their family where it remained virtually unopened and unread for the past 80 plus years. I use the word ‘virtually' because one section does show signs of being read. Appropriately, that section -- the last one in Joyce's masterpiece -- is considered the most obscene.