Dramatis Personae I — Telemachus

Cranly makes his first appearance in Portrait of the Artist as a Young Man and is based on Joyce's friend from university, John Frances Byrne. A devoutly religious young man, Cranly is both well-spoken and intelligent. Stephen Dedalus describes him as a pale, handsome face with large, dark eyes and an athletic body. Cranly talks with Stephen at length during the end of Portrait, especially about Stephen's decision to abandon Catholicism (it is to Cranly that Stephen makes his infamous "silence, exile, and cunning" speech). During that exchange, he often amicably—with an "elder's affection"—grabs hold of Stephen's arm, contact Stephen seems to relish.
That selfsame contact marks Cranly's first appearance in Ulysses. In Telemachus, Buck Mulligan links arms with Stephen and parades him around the top of the tower (at page 18), and Stephen thinks simply "Cranly's arm." It's a moment of stark contrast between Cranly and Mulligan, for while Mulligan has replaced Cranly's role in Stephen's life, he has failed to do so with the same level of care and love.
Cranly also appears in Nestor and twice in Scylla and Charybdis, where Stephen also remembers his smile. 
Stephen Dedalus is the Telemachus to Leopold Bloom's Odysseus and, more loosely, an analogue for both Shakespeare's Hamlet and Ovid's Dedalus. Joyce saw himself in Dedalus, too. Like Hamlet, Stephen is a brooding but brilliant young man that lives mostly in his own head. Like Dedalus, he is "trapped" in a tower, but yearns to soar above the confines of his world. Stephen first appeared as the protagonist of A Portrait of the Artist as a Young Man, which serves as something of a prequel to the role of Dedalus in Ulysses.

Ulysses opens with Stephen mourning his mother, May Dedalus. Those who've read Portrait  will remember how that book ended with Stephen refusing to take Easter commune, despite his mother's earnest wishes. This rebellion bleeds into Ulysses, where Stephen has refused to kneel down and pray by his dying mother's side.   

Dedalus works as a teacher while unproductively developing his own private thoughts on religion and literature, such as his famed theory on Hamlet. He is in some debt to his friend Buck Mulligan. Stephen Dedalus is the second character to appear in Ulysses, on page 5 of the comic.  

Fun Fact: Rob's drawing of Stephen was inspired by his friend, the Philadelphian actor Allen Radway. "I never imagined him as anyone else," Rob says.

Mrs. May (Mary) Dedalus is Stephen Dedalus' recently-deceased mother. A devout Catholic, much of the end of A Portrait of the Artist as a Young Man and the beginning of Ulysses focuses on the pain that Stephen's abandonment of Catholicism caused Mrs. Dedalus. Mrs. Dedalus appears only in memories throughout the book: mostly in Stephen's but also in Leopold Bloom's reminder to himself that Stephen has recently lost his mother and Simon Dedalus his wife.
Haines is a well-off Englishman from Oxford, staying with Buck Mulligan and Stephen Dedalus at Martello Tower. A secondary character that first appears in Telemachus, Stephen and Mulligan discuss him beginning on page 8 of the comic but he does not appear bodily until page 31.   Haines seems to be in Ireland to satisfy a kind of curiosity about the culture there. He sympathizes superficially with the problems English colonialism has caused there, but distances himself from them as well, saying “history is to blame.” He speaks Gaelic and dabbles both in religion and literature. But, when he attempts to engage Stephen on these topics, he finds himself rather outmatched.   Stephen thinks of Haines as a kind of usurper, taking his place at Martello tower. Fun Fact: Rob modelled Haines off of late-night comedian Stephen Colbert.
The Man in the Forty-Foot Hole.
The Milk Woman is an unnamed, minor character appearing only in Telemachus—starting on page 36 of the comic. As her moniker suggests, she delivers a quart of milk to Haines, Buck Mulligan, and Stephen Dedalus for their breakfast at Martello Tower. A woman whose body is diminished with age, Stephen envisions her at once as a poor old woman deftly milking her cows in the field, a witch upon a toadstool, and as a kind of messenger: perhaps an analogue for Athena, who appears to Telemachus as an old man in the first book of The Odyssey. Her act of servitude—harvesting and selling the wholesome, nourishing products of Irish agriculture—makes her a “common cuckquean” in Stephen’s eyes: both to “her conqueror” (Haines, the Englishman) and her “gay betrayer” (the joyful Mulligan, choosing English Haines over Irish Dedalus). She is particularly impressed with Mulligan’s status as a medical student.   Hanes likely sees her as an iconic Irish peasant, and he tries (unsuccessfully) to speak Gaelic with her. She mistakes the language for French, which rather destroys the image. Nevertheless, she finds the language beautiful and regrets her inability to speak it. Fun Fact: Rob's visualization of the Milk Woman initially earned the project censorship from Apple!
Buck Mulligan is Stephen Dedalus' erstwhile friend and roommate at Martello Tower. Mulligan is a medical student with a seemingly well-off aunt acting as his patron. He enjoys living, especially food and drink, and seems unable to take anything too seriously: even his wardrobe, which ranges from bathrobes to panama hats.