First published in France in 1922, it was soon declared to be obscene in both Britain and the United States; copies had to be smuggled in (one innovative British couple hid theirs in a box of "sanitary napkins"!). A famous court case in 1933 lifted the ban in the states, after which Random House brought out its first edition, seen here in the hands of Marilyn Monroe.
It wasn't easy reading. The "stream of consciousness" style dumped the internal thoughts of the characters onto the page in a sort of real-time sequence, connected as much by personal association as by plot. Guidebooks on how to read Ulysses sprang up, with Stuart Gilbert's being the first and best-known. And, more recently, disputes over textual variations -- the original edition was set by printers in Dijon who spoke no English, and subsequent editions did an imperfect job of implementing Joyce's corrections -- has led to duelling versions. I myself recommend the first edition of 1922, which, as its copyright is now expired, can be had in an affordable paperback from Dover Books.
In The Graphic Canon, we have two Ulysseses --the first by Robert Berry and Josh Levitas, the secind by David Lasky. Berry and Levitas offer a lush, colorful version, filled with the melodious phrases of the original novel; in contrast, Lasky offers a black-and-white and nearly wordless one; what few words there are are paraphrased. Barry and Levitas are adapting the full novel as an iPad app, under the title Ulysses Seen, and so far, theirs follows the text quite closely, though it acknowledges in its very title that seeing is quite different from reading. Lasky's stab at Joyce's novel appears to be just that; he's best known for his graphic history of the Carter Family, regarded as among the founders of modern Country music.
It could be argued that a big, wordy, and (purportedly) difficult classic could use a lighter, more visual treatment -- or else that, without its language, Ulysses isn't, well ... Ulysses. Which side are you on?