By Jove!

Throughout the novel, Joyce makes quite a few allusions to classical/classically-based works, from the Father's description of Hell (Dante's Inferno), to Stephen's very name and his epiphany. After Stephen’s revelation at the end of Chapter 4, we see Stephen being open about his doubts of Christianity. He no longer possesses that devotion (if you can call it that) to God he once had. He has lost faith.

Much of Stephen's earlier life was centered around the Church. Now what? Is he that artist of independent spirit completely separate from the rest of the world? This might be a stretch, but I would say that Stephen's revelation reflects a change in his source of inspiration. After his revelation, I think Stephen turns to the classics for inspiration. As his friends tease him, he realizes the significance of his last name, and all the symbolism that comes with it (flight, freedom, the artificer, etc...). He begins to view the world differently and becomes the “artist”, like Daedalus of Greek myth. Also, much of his aesthetic theory is based on Aristotle and Aquinas (who drew on Greek philosophy for a lot his work). The last line of his journal even says "Old father, old artificer, stand me now and ever in good stead." Perhaps the "father" he mentions refers to God (maybe he still has some faith), Daedalus of Greek myth, or even Simon Dedalus. Either way, he sees this father figure as an artificer, like Daedalus of Greek myth. It shows his changed view of the world. Earlier he was under a vengeful God and much of his faith in this God was through fear. Now, this new father figure is a creator, an artificer. Stephen sees him in a much more positive light and feels free to view the world as he sees fit, as opposed to mortifying his senses in his devotion to the Christian God.

Pride

Throughout Stephen's life, from childhood to adolescence, from extreme sin to piety, Stephen maintains one major flaw: pride. In class, we discussed how as a child Stephen seems to sense something unique about himself, something that makes him different (if not better) than his fellows. We see him imagining his own funeral as he lays sick in bed, giving himself much importance. Perhaps this is only a childlike self-fixation, but I think it develops into the pride of his later years. Later on, in Blackrock, we see Stephen musing about a great transformation that will happen to him. As we talked about in class, Stephen adopts a passive attitude to this change, believing that he doesn't need to do anything to be transformed: "Weakness and timidity and inexperience would fall from him in that magic moment." There is some arrogance in Stephen's belief that he is almost destined to become greater.
He soon writes his first poem "To E---- C---" and stares at himself in the mirror. Perhaps he thinks of himself as already changed and is admiring the new him. We later see him and his father on a train. Stephen is annoyed by his father's sentimentality as he reminisces about his younger days. Stephen feels that his father is acting immaturely. He thinks of himself as better than his father in some ways. I would say that it is at this point that Stephen's sense of being special develops into pride.
We then see Stephen enter a life of sin. He feels too lost, too self-pitying, too prideful to seek God's forgiveness: "A certain pride, a certain awe, withheld him from offering to God even one prayer at night though he knew it was in God's power to...hurl his soul hellward...His pride in his own sin...told him his offence was too grievous to be atoned for..." He is also contemptuous of his classmates.
Eventually, Stephen seeks God's forgiveness and feels renewed and pure. Perhaps now he won't be so arrogant? Not so. As he enters a life of piety and asceticism, we see he still hasn't reigned in his sense of pride. He feels disdainfully irritated at those who distract him from his prayers, but at the same time knows this irritation is characteristic of his teachers, and does not want to be like them. Like how Stephen "talked" directly to God during his life of sin, he views his life of piety as a one-on-one battle between him and the Devil as he defends himself from temptation.
Even after meeting another mysterious women in a magical transformation, we see him still arrogant. He is quite flippant about his university education, overall feeling that he is not learning much. We see a new aspect of Stephen's pride as he talks to some fellow students. For not taking an Irish language class, Davin calls Stephen out on not being an Irish nationalist like himself: "In your heart you are an Irishman but your pride is too powerful."
Already nearing the end of the novel, we see that Stephen remains prideful. Maybe by the end we will see him lose his arrogance. Or perhaps he will mold his pride into a defining trait as an artist.

Joyce's Divine Comedy

Midway upon the journey of our life
I found myself within a forest dark,
For the straightforward pathway had been lost.

                       Dante's Inferno, Canto I, lines 1-3


So Stephen finds himself in Chapter 3. After his first sexual experience, Stephen feels lost. He is full of sin--from lust the rest followed. "His pride in his own sin, his loveless awe of God, told him that his offence was too grievous to be atoned for in whole or in part by a false homage to the All-seeing and All-knowing." He is indeed "within a forest dark." Then, like Dante's Virgil, the school rector announces a retreat--a spiritual journey.

Although Chapter 3 could be argued to mainly reference Dante's Inferno (with the vivid descriptions of Hell), I would say that this chapter reflects the whole of Dante's Divine Comedy: from Hell to Paradise, from spiritual abjection to spiritual redemption.

The second part of Chapter 3 hurls us hellward. Soon after Father Arnall discusses the retreat, we see how Stephen suffers in mental anguish as he imagines Judgement Day. Already, even before the Father's sermon, Stephen is experiencing Hell--another step in Stephen's journey to Paradise. Then we get Father Arnall's sermon on Hell. Dante's Inferno is famous for its fiery and vivid description of Hell: its organization, its punishments, even its denizens. Father Arnall might as well be Dante. He masterfully describes Hell, with its "never ending storm of darkness, dark flames and dark smoke of burning brimstone, amid which the bodies are heaped one upon another without even a glimpse of air." Stephen is on a tour through Hell. Thanks to Stephen's rich imagination, as Father Arnall explains the tortures of Hell, it is almost as if we experience them ourselves. After a break, Father Arnall discusses the spiritual torments of Hell. Again, although it is just a description, we see Stephen suffering and experiencing these pains himself. At the end, he and the other boys pray to God for forgiveness. 

Stephen finishes his tour through Hell alone. Full of fear, he goes to his room and falls asleep. This fear manifests itself in a nightmare where Stephen is surrounded by demons. When he awakes, he prays and cries. He is ready to enter Purgatory and cleanse himself. As he heads out we see he realizes the gravity of his sins. Finally, he enters Church Street Chapel and makes a heartfelt confession to the priest, who forgives him. Free of sin, Stephen enters Paradise and the next stage of his life:

"Another life! A life of grace and virtue and happiness! It was true. It was not a dream from which he would wake. The past was past."