As other answers here have noted, Dante's Divine Comedy seems to contain a catalog of themes, but as a quest story, its overarching one is the individual's journey to salvation. Salvation, in the medieval Christian sense, means union with God in Paradise, but along that journey are several moments that affirm what salvation requires, and this systematic poem is constructed on these moments of supporting themes.
At the end of each of the three epic books, Dante sees light, so we can understand the theme involving enlightenment. In Inferno, this light seems to be the stars, but in Paradisio, he recognizes that what he had glimpsed are actually the souls in Heaven reflecting God's light. Enlightenment comes, in a somewhat Platonic (e.g. "Allegory of the Cave") sense, from turning away from shadows or false reality to see the nature of human sin and virtue as they seem from a Divine perspective.
In Inferno, for instance, Dante the Pilgrim must confront the contrapasso of multiple sins in order to see what they really are. Each sinner receives a punishment that metaphorically represents the precise error within the sin. The sinners get what they really wanted all along, and they are punished by the knowledge that they chose the wrong thing. The knowledge as well as the contrapasso create the punishment, for in the Inferno, they cannot make another choice and are trapped by their own malevolent desires. The sin of lust, for instance, leads to being swept eternally in a hurricane. This perversion of real love, which uses others's bodies for one's own pleasure, involves a desire for the false feeling of being swept away by passion, as Franscesca describes. Canto by canto, Dante offers images of cosmic irony showing that sinners have loved the wrong things or loved incorrectly. In doing so, they distort their appetites, their passions, and their intellect, committing sins of excess, malice, or fraud. Dante the Pilgrim must come to an understanding of the nature of each of the sins he encounters in order to see the ugliness of each one, knowingly reject it, and move on. In this way, one could say that the two important themes within the Comedy are right knowledge (wisdom) and love—attributes Dante gives to God early in Inferno. As Dante journeys through Purgatorio, he sees souls cleansing themselves of small distortions in their knowledge and love, and in Paradisio, souls are fully aligned with the virtue they most love, thus placed in a corresponding circle.
A secondary theme, but one that Dante seems to have been highly invested in, involves the role of poetry or art to bring the soul to salvation. The poem repeatedly meditates on its own practice. In Inferno, for instance, Dante the Pilgrim seems mightily troubled when he encounters sinners damned through art—Franscesca was a bad reader, Brunetto Latini sought to "live" through his creative work the Tresor, but he ends up among sodomites whose fertility is squandered, and Ugolino uses narrative as a form of revenge. Each of these are dangers that Dante the Poet faces as he embarks on his own poetic journey through the Comedy and a recurrent temptation he must overcome to produce an epic that gives both fame and spiritual immortality to the poet.