It is, of course, Iago's revenge that provides the catalyst for virtually everything that happens in the play. It is his deep resentment at his relatively low status in life that drives him on, making him determined to destroy all those, including his master Othello, who represent a social system which has held him back all these years.

Iago's thirst for vengeance is all the more dangerous in that it shows no signs of being assuaged. There's something positively demonic about it; the desire for revenge controls Iago to such an extent that it's doubtful he could break free from its iron grip even if he wanted to.

As for forgiveness, a particularly heart-rending example comes when Desdemona forgives Othello with her dying breath:

Nobody. I myself. Farewell.

Commend me to my kind lord. Oh, farewell! (Act V Scene ii).

The main plot of William Shakespeare's Othello is typical of the genre of the revenge tragedy in having revenge as its main theme. The central example of the revenge theme is Iago, who is motivated to destroy Othello in revenge for Othello's preferment of Cassio. Iago's schemes also include revenge against Cassio. Othello's murder of Desdemona is also motivated by revenge for his being cuckolded (although that was actually a fabrication by Iago and did not happen). For forgiveness, at the end of the play, Othello correctly places blame and forgives Desdemona and Cassio. Brabantio partially forgives Desdemona, and the Duke advocates forgiveness at the marriage to Othello. Cassio forgives Othello in his final words praising him.