The number three, which was thought to have divine significance, structures The Divine Comedy in a repeated way. Three beasts—the lion, the leopard, and the she-wolf—block Dante's path to paradise. The dog Cerberus has three heads. There are three kinds of sin in hell—lack of self control, violent behavior, and lying or fraud—and each type occupies three levels of hell. Further, Satan himself has three faces in a grotesque parody of the trinity. After life, there are three states of being: torment, preparation for heaven, and heaven.
Paradise is set up in threes, with nine levels, just like hell, and the poem itself is written in terza rima, three-line stanzas. All of this reinforces a main theme of the poem, which is that the universe is orderly and completely under divine control. People can try to rebel against God, but in the end everyone falls into his proper place in a carefully conceived cosmos in which justice is enacted.
The sequence of the poem, which has Dante first going through hell, then purgatory, and only then ascending up the mountain to heaven, reinforces another theme: that one needs to be humbled and aware of one's sin—and sin in general—to be able to truly perceive and receive the gifts of paradise. Dante has lessons to learn before he can be reunited with Beatrice and approach what is truly holy.