Short answers, pulled from the story.
Ulysses was first published in Paris on the 2nd of February 1922 by Sylvia Beach's Shakespeare and Company. That date was Joyce's fortieth birthday. The novel had previously been partially serialised in the American journal The Little Review from March 1918 to December 1920.
Ulysses takes place on the 16th of June 1904, a single day in Dublin. That date is now celebrated annually by fans of the novel as Bloomsday.
Ulysses was effectively banned in the United States after a 1921 trial found the journal The Little Review obscene for serialising the novel's "Nausicaa" episode. The case was brought by John S. Sumner of the New York Society for the Suppression of Vice under the Comstock Act of 1873. The ban was overturned in 1933 when U.S. District Judge John M. Woolsey ruled the book was not pornographic.
The novel's eighteen episodes roughly correspond to episodes in Homer's Odyssey. Leopold Bloom corresponds to Odysseus, Molly Bloom to Penelope, and Stephen Dedalus to Telemachus. Joyce structured the novel's three parts to mirror the Odyssey's tripartite division, and the episode titles familiar to readers today come from private schemata Joyce sent to Carlo Linati and Stuart Gilbert.
According to Joyce scholar Jack Dalton, the first edition of Ulysses contained over two thousand errors. Correcting them across later editions proved difficult because separating genuine printing mistakes from Joyce's own deliberate textual puzzles was often impossible.
On Bloomsday 1982, RTÉ, Ireland's national broadcaster, aired a full-cast unabridged dramatised radio production of Ulysses that ran uninterrupted for twenty-nine hours and forty-five minutes. An unabridged reading by Jim Norton and Marcella Riordan was later released by Naxos Records on twenty-two audio CDs in 2004.