What is the importance/use of furies in Dante's Inferno?
I understand the symbolism that the furies provide as the "karma" represented in the ancient Greek times (especially the household). However I'm having trouble understanding Dante's use of these ancient characters in his work: the of furies in this work has what aim.
As the e-notes study guide notes, these mythological avengers of great crimes represent a a guilty conscience. It is signifcant that they shout out to Medusa to come up and turn the poets into stone. Dorothy Sayers comments that allegorically the furies represent "fruitless remorse that does not lead to repentance" while Medusa "is the image of despair which so hardens the heart that it becomes powerless to repent" (Sayers trans., Penguin Classics, 127). The notion of the mind turning to stone and blindness (i.e., when Virgil covers the Pilgrim's eyes) are central motifs; the entire poem is really about acquiring the proper vision of things, of having a mind that is united to God's.
Secondly, because three furies are named, this is another anti-Trinity. Since they are female, they are an infernal counterpart to the three heavenly ladies (Blessed Virgin Mary, St. Lucy, and Beatrice) mentioned in Canto 2.
Finally, the snakes that are coiled around their waists not only is a satanic image, but also is an infernal contrast to the cord that we learn (in Canto 16) is around the Pilgrim's waist.