The novel opens with Buck Mulligan shaving atop Martello Tower and mockingly re-enacting the Catholic Mass.
He jokes with Stephen about their absurd names and suggests that they need to Hellenize (make more Greek) Ireland.
Buck Mulligan gives Stephen a hard time for not praying at the bedside of his mother. He says that maybe Stephen is insane.
When Stephen tells Buck Mulligan how angry he is that he (Mulligan) referred to his mother disrespectfully, Mulligan becomes indignant and says Stephen is an impossible person.
They go down and have breakfast with Haines.
When the milk woman comes, Buck Mulligan treats her disrespectfully.
He tells Stephen to hurry off to school and bring them some money.
Haines is thinking of making a book of Irish sayings, and Buck Mulligan tells him that he should wait until he hears Stephen's Hamlet theory.
They go down to the bay and Buck Mulligan goes swimming. When Stephen leaves, Buck Mulligan asks him for the Tower key and twopence.
Episode 6: Hades
When Bloom sees Stephen in the street and points him out to his father, Simon begins to complain of the company Stephen keeps.
He thinks that Mulligan is a scoundrel, and says that one day he will write a letter to Mulligan's Aunt telling her as much.
Episode 9: Scylla and Charybdis
Mulligan comes in late, while Stephen is presenting his Hamlet argument at the National Library. He gives Stephen a hard time for ditching him and Haines at the Ship (they were supposed to meet at noon).
They joke about a time that Stephen urinated on the playwright John Synge's doorstep.
When Stephen concludes his theory, Mulligan begins crying "Eureka!". He runs over and jots down the cast list for a silly play called "Everyman His own Wife or A Honeymoon in the Hand (a national immorality in three orgasms)" (9.435).
It's a parody of Stephen's.
When Stephen and Mulligan pass out over the Library, Mulligan kids Stephen that Bloom is gay and is interested in him.
Episode 10: The Wandering Rocks
Shortly after 3pm, Buck Mulligan and Haines are getting coffee.
Mulligan points out John Howard Parnell, Charles Stewart's brother, playing chess in the corner.
Mulligan tells Haines that he missed Stephen's Hamlet discussion, and Haines says Shakespeare is "the happy hunting-ground of all minds that have lost their balance" (10.582).
Mulligan says Stephen lost his wits due to repeatedly being shown visions of hell as a child. He predicts that Stephen will write something important in ten years.
Episode 14: Oxen of the Sun
A bit after 10pm, on his way to the National Maternity Hospital, Buck Mulligan bumps into Alec Bannon, who has just returned from Mullingar. He says that he met a "skittish heifer" there, referring to Milly Bloom.
Mulligan appears with Alec Bannon. A bunch of medical doctors, students, and men about town (including Bloom and Stephen) are gathered in a room making merry (except for Bloom and Stephen). Mulligan passes around some cards he has had made, which read: "Mr. Malachi Mulligan, Fertiliser and Incubator" (14.29).
Mulligan embellishes on his joke at length, describing how he will set up a clinic called Omphalos on Lambay Island. There he will fertilise any young woman who comes looking, and won't even take a penny for his pains. The men get a big kick out of it.
Mr. Dixon teases Mulligan about his girth in medical student talk. Mulligan pats his stomach and says, "There's a belly that never bore a bastard" (14.30). They all laugh uproariously.
Mulligan tells a mock-ghost story involving Haines, in which Mulligan confesses to being the real murderer of Sam Childs. Throughout, he makes use of Stephen's saying from the day, using them as if they are his own. In particular, he parodies Stephen's Hamlet theory.
Later, he proceeds to Burke's pub with the rest of the men.
Episode 15: Circe
Mulligan appears twice in "Circe." First, he appears as a medical professional offering testimony on Bloom's behalf in Bloom's long court dream sequence. Mulligan suggests a number of sexual abnormalities that might account for Bloom's behavior.
Second, when Stephen has an image of his mother May, Mulligan appears in a jester's uniform. From up on high, he laughs at how Stephen's beastly mother is dead and mocks Stephen's horrific situation.
Episode 16: Eumaeus
Bloom suggests to Stephen that Mulligan may have slipped something in his drink earlier.
We learn that Mulligan and Haines took the key from Stephen and slipped away back to Martello Tower.
Bloom tells Stephen that Mulligan seems to be jealous of him and is taking advantage of him at every opportunity.