Inferno is a funnel dug beneath Jerusalem, which descends in nine circles to the center of the Earth. It has 34 cantos in linked-rhyme tercets, the terza rima, and the first serves as a prologue to the whole poem. The circles follow the order that Virgil explains in Canto XI.
The first circle is Limbo, where the virtuous who were not baptized dwell, along with Virgil himself; the punishment is the absence of hope, not torment. Circles 2 to 5 punish incontinence, in which appetite overcame reason: lust, gluttony, avarice and prodigality, and wrath. Circles 6 and 7 lie within the city of Dis: in the sixth, the heretics, in tombs of fire; in the seventh, the violent, against their neighbor, against themselves, and against God and nature.
The eighth circle is Malebolge, ten ditches of dark stone around a well, where fraud is punished against those who did not trust in particular: seduction, flattery, simony, divination, barratry, hypocrisy, theft, fraudulent counsel, discord and falsification. The ninth is Cocytus, the lake of ice of treachery, which divides into four zones, Caina, Antenora, Ptolomea and Judecca, with Lucifer at the center.
The logic of the order is that the sins of desire are the lightest and those of corrupted intelligence the gravest. That is why the lustful man stays near the entrance and the traitor at the bottom.