Part 1: The Telemachiad
Now, you'd think that since Ulysses is modeled on the Odyssey, which is pretty much the classic quest story of all time, this should be easy to map out. The fact of the matter is that it's not. There are a number of different ways to do this plot analysis. We just picked one, but there are other valid ones as well. Though Bloom (the Odysseus figure) does not even appear until after The Telemachiad, we here have another hero, Stephen Dedalus (the Telemachus figure) for whom life has become nearly intolerable in Dublin. Without even knowing it, he sets out to wander through Dublin with the hope of meeting someone like Leopold Bloom, someone that can give him some guidance, help him put things in perspective, and make him feel a little less cut-off from the world.
Part 2: The Wanderings of Ulysses
The majority of the book consists of Bloom's (and Stephen's) wanderings through Dublin where they encounter a number of different challenges: Bloom must undergo an encounter with death and the underworld at Dignam's funeral. Stephen must navigate between the Scylla of Aristotelian literary philosophy and the Charybdis of Platonic philosophy. Bloom must confront the one-eyed nature of prejudice in "Cyclops." Both Stephen and Bloom must resist the spell of the Circe-like prostitute madame, Bella Cohen. Their journeys are decidedly more meandering than in the Odyssey. One critic joked that whereas Odysseus spends the entire epic fighting to get back to his wife, Bloom spends the whole book looking for reasons not to go home to his wife. Yet, though they aren't quite sure what they're looking for, both Bloom and Stephen are searching for something. For the latter it might be called human-connectedness, and for the former it might be called the spirit of resignation or forgiveness.
Arrival and Frustration
Part 3: Homecoming: Eumaeus, Ithaca
The last part of the book is named Homecoming, so we get the sense that after "Circe," the majority of the day's challenges have passed. For Bloom, in particular, saving Stephen from the English constable has put him in a good mood and he is eager to get to know his knew companion. Stephen, though safe from serious legal trouble, is still quite drunk and is in a foul mood as Bloom tries to get a real conversation going. The two of them go to Bloom's home together, but as Stephen leaves, Bloom gets the sense that this won't actually be the blossoming of an ideal friendship. Inside, he sees how his house has been re-arranged by Boylan and Molly, and he becomes glum as he thinks of his father's suicide. Whatever he is looking for, he hasn't quite found it.
The Final Ordeals
Part 3: Homecoming: Ithaca, Penelope
The final ordeals might be said to come at the end of "Ithaca," after Stephen leaves for the night. Bloom is here confronted with unmistakable evidence of his wife's affair, and realizes that he has been avoiding the thought for most of the day. Thinking of his father's suicide, he again is brought to the brink of despair, but he gradually begins to sort through his feelings and come to a sense of equanimity that allows him to mount the stairs and crawl into bed with his wife. Yet the perspective that is missing in the Odyssey is Penelope's, and we here end with Molly's thoughts on Bloom. We are forced to re-evaluate the character we thought we had come to know, and wait to see how he will fare in her judgment.
Part 3: Homecoming: End of Penelope: Memory of Bloom's Proposal
Bloom's day ends after "Ithaca," as he kisses his wife's rump and nods off to sleep. He has come to some sense of understanding about his wife's affair and his role in it, and has found a way to live with it (at least for this evening). Yet Molly's long stream-of-consciousness soliloquy seems to again put Bloom at risk, and it is unclear whether or not Molly will ultimately approve of her husband or not. In the final pages, however, we see a triumph for Bloom. Molly's last thoughts of the day are for her husband. On a broader note, we see a ray of happiness come into the novel. There is real empathy between husband and wife, and despite all its perils, the novel ends with a resounding affirmation of married life: yes I will Yes.