My English edition was the Penguin Classics 2000 reprint. I had much help from Ulysses Annotated by Don Gifford and Robert Seidman, second edition, 1988.
The internal cohesion of the book is truly astonishing. Nothing happens which is not related to something else. Any detail given matters at some point, and a casual sentence like "I was just going to throw it away" triggers a whole avalanche of events. You end up with a huge jigsaw puzzle which you are supposed to put together. Some pieces are missing though. Nobody knows what "U.P. up" means, nor who "the man in the brown macintosh" is.
The novel is divided in eighteen episodes with titles referring to Homer's Odyssee. The analogy is somewhat distorted, to say the least, and the identification of Molly with the faithful Penelope is one of the book's many funny aspects. My favourite episodes are (in descending order):
18. Penelope. Molly's hilarious monolog, in eight endless chaotic sentences. (Partially phrased loose associations inside a person's head are frequent in Ulysses.)
This final episode is also what Marilyn Monroe is seen reading above. (Not her own choice of literature, but Molly's Monolog was an assignment for Actor's Studio, where she had turned to become a serious actress. No doubt she has skipped the seventeen preceding episodes, which were not included in her homework.)
13. Nausicaa. Inside the head of a girl seducing Bloom, with good result, from a distance.
17. Ithaca. Bloom's orderly mind exposed in an elaborate catechism with questions and answers, ending in a Q.E.D. mark.
Some episodes are very boring and I found 9. Scylla and Charybdis the worst. But then, Joyce being who he is, maybe they were intended to be boring.
Each episode has its own narrator and style (some have several), and in places writing is very obscure. The net result is, that it's difficult to know what happens. I was quite relieved to find (here, for instance) the events linearly ordered by someone who has managed to put the pieces together. I know, meandering mystery is part of any detective story, but at The End you are entitled to know the whole truth.
Now for some criticism. Bach's Well Tempered Clavier is very learned (it wanders twice through all 24 major and minor keys, one after the other) but to those unaware of this display of craftsmanship it's "just" beautiful music. With Joyce, it's impossible to ignore the display of styles, because they are overwhelmingly present, to the point of obscuring the content. I feel Joyce overestimates what readers are willing to invest in order to understand a novel. This is bad, in the same way that Schönberg has overestimated what the human mind can grasp from well-designed but totally counterintuitive music. Joyce's wife asked her husband Why don't you write books people can read? Indeed, why make readers struggle, even suffer? Call me an ignoramus, but I can't refrain thinking what Ulysses might have been if it had been mounted in a more conventional way. (I know, it's some kind of blasphemous nonsense. Back to eulogy.)
Ulysses is consistent up to perfection. (Yes, I've written the same sentence here.) Let me give one example out of many. Among the actors in the dreamlike play of Episode 15, we find Bloom's grandfather, an Hungarian Jew called Lipoti Virag. But when he introduces himself he does it the Hungarian way: Virag Lipoti, last name first! Times, places, events, everything fits. Nevertheless, here comes a minor issue. With a lesser author than Joyce I would call it an error (well, "character error" is more appropriate) but with Joyce, one had better be prudent.
Bloom's unlikely mistake
Howth. Bailey light. Two, four, six, eight, nine. See. Has to change or they might think it a house. Wreckers. Grace Darling. People afraid of the dark. Also glowworms, cyclists: lightingup time. Jewels diamonds flash better. Light is a kind of reassuring. Not going to hurt you. Better now of course than long ago. Country roads. Run you through the small guts for nothing. Still two types there are you bob against. Scowl or smile. Pardon! Not at all. Best time to spray plants too in the shade after the sun. Some light still. Red rays are longest. Roygbiv Vance taught us: red, orange, yellow, green, blue, indigo, violet. A star I see. Venus? Can't tell yet. Two, when three it's night. (Bloom's thoughts, Nausicaa, p.490 in Penguin Classics.)
The place: Sandymount Strand, the beach beneath the seawall near the foot of Leahy's Terrace (Gifford p.384). The date: June 16, 1904, shortly after sunset. In the local newspaper, sunset was given at 8:27 P.M. (Gifford 13.2), which is confirmed by this listing (courtesy of Sky View Café).
Bloom notices "lightingup time" for cyclists which was, on that particular day, 9:17 P.M. (Gifford 13.1070). So, let's say we overhear Bloom at 9:20 P.M. He rightly observes "Some light still". It's a strange thought though, because the sky above Dublin doesn't become dark in June. The sun does sink below the horizon, but not deep enough, and evening twilight simply merges with dawn. A scientific mind like Bloom, who includes astronomy in his catechism and owns an Astronomy Handbook, would certainly be aware of that. But let's read on. In the twilight he notices a first star. Where is he looking? Probably, as any person on the beach would, to the sea, all the more since there (in the East, look Leahy's Terrace up in Google Maps for the setting) the sky is darkest. Here is what Bloom saw at 9:20 P.M. (courtesy of Sky View Café); if you look at the bottom part, you look towards the sea.
So Bloom thinks it might be Venus he sees, but he needs more stars to be sure about the constellation. Now wait a minute. To be first visible, Bloom's star must be among the brightest ones in the sky. Now these are Vega in the East, Arcturus and Spica in the South. None of these would make a knowledgeable man like Bloom think of Venus, not for a second: they are far away from the Sun, and Arcturus is also very red. Everybody knows that Venus is never seen far from the sun, which has just sunk below the northwestern horizon (lighter in the picture above). Regulus is nearer but is not bright enough and too low to be observable above Leahy's Terrace in the west. James?
Gifford's comment 13.1076 is: The evening star on 16 June 1904 would have been Saturn, not Venus. Actually, Saturn did'nt rise until after midnight. And then, only Venus is ever called morning or evening star.
P.S. With all its modernistic aspects, Ulysses is anything but unreadable as I, who read it three times, can testify. The unreadable book by Joyce is the next one, Finnegans (sic) Wake. Here, he let go completely or (phrased differently) finally abandoned to a madness he had been flirting with before with at least some restrain. I bought the book, because some day I will want to see for myself that it is unreadable. Quarks, subatomic particles occurring only in threesomes, owe their name to it, because that's where Murray Gell-Man found the suitable phrase Three quarks for Muster Mark!