Stephen Dedalus is like Telemachus (from The Odyssey), a thoughtful young man with no real father figure. Stephen's mother has died and he is alienated from his religion and his home country (Ireland). He is well read and likes discussing literature and poetry. He is searching for meaning in his life and a place and/or profession. He finds a father figure in Leopold but eventually returns to the tower in which we find him at the start of the novel. He is not just trying to "find himself"; he's also trying to understand the world. He therefore comes across as depressed and overly sensitive, somewhat like Hamlet. He feels like an outsider, disconnected—the jumpy, frenetic style of the novel's narration and dialogue underscore his feelings of disconnection.
Leopold is the symbolic Ulysses/Odysseus and he has lost a young son (Rudy). Therefore, he longs to be a father figure and this is evident when he encounters Stephen. His wife cheats on him, but this is because they both find their daily life to be dull. Leopold is very sensitive and thoughtful (like Stephen). He, like his wife, longs for an escape from his daily life and has thoughts of affairs with other women and indulges in these fantasies on his own. Leopold is the "everyman." Both Stephen and Leopold are modern men looking for something more in life. (This characterization of Leopold also conjures Tennyson's poem "Ulysses" which speaks of an older Ulysses bored with his life at home with his wife; he longs for something more adventurous.)
Molly is the symbolic Penelope, Ulysses'/Odysseus' wife. But whereas Penelope is faithful, Molly cheats on Leopold. She is an attractive professional singer. Molly is presented as this attractive, adulterous woman through much of the novel—that is until we read her thoughts. Molly is simply acting out in defiance of a loveless (or sexless) marriage. She is typically more outgoing and demonstrative with her feelings and Leopold is not. So, we can sympathize with her need to seek that love elsewhere. She understands how to play different roles in life; this makes her seem like a hypocrite but also like someone who understands how to function in different modes of life. This notion also underscores the use of stream of consciousness and the frenetic narrative techniques in the book. It suggests that Molly, Leopold, and Stephen (and anyone really) are multi-dimensional individuals.
Although quite different in their own ways, each of the three main characters seeks to find something more meaningful, something more interesting beyond their daily, typical lives. This is the Modernist search for a grand narrative (story, idea, role): something to make sense of living in a fragmented world, to find a place where/when we fit in.
1. Leopold Bloom
Bloom's character is an outsider due to his disinterest in drinking and gossiping; A popular pass time for his counterparts. He embodies the insularity of Ireland during the time period, but is quite content with his social exclusion.
2. Molly Bloom
It is easy to focus on her monologue that puts a certain distaste in our mouth, but it is important to take a step back and analyze her character. She is an outgoing extrovert who is prideful of her husband but faces a lack of reciprocal love from his. This places more blame on her husband for the crumbling of their marriage.
3. Stephen Dedalus
We first meet Dedalus in A Portrait of the Artist as Young Man. We are then reintroduced 2 years later in this novel. He is distant and his lack of cleanliness only embodies his clear distinction from the rest of the world. He is disconnected and an unsympathetic character. That is until we understand his struggle for agency in defining his identity.