Two of the most common themes associated with Othello are jealousy/revenge and appearance versus reality (or "seeming"). Both of these are common themes in Shakespeare's plays, ones that you will see re-investigated over and over.
Jealousy appears in Act I, scene i when Iago is talking about being passed over for promotion. Othello has promoted Cassio instead of Iago. Iago says:
I know my price, I am worth no worse a place.
But he, as loving his own pride and purposes,
Evades them. . .for "Certes," says he,
"I have already chosen my officer,"
And what was he?. . .
One Michael Cassio. . .mere prattle without practice
Is all his soldiership.
So, Iago shows his reason for jealousy towards Cassio, and goes on to explain his revenge against Othello.
Othello also displays his jealousy and thirst for revenge. Iago has led him into believing that Cassio is having an affair with his wife, Desdemona. In Act IV, scene i, once Othello thinks he has the proof, his thoughts turn to murder as his revenge:
I will chop her into messes. . .Cuckold me!
O, tis foul in her.
With mine officer!
And so, Othello's jealousy overtakes everything else and leads him to kill the thing he loves best.
The theme of appearance versus reality is actually shown in both of these same characters. Iago decides to hide how he really feels about being passed over, appearing to loyally follow the man (Othello) that he hates. Back again in Act I, scene i, he says:
In following him, I follow but myself.
Heaven is my judge, not I for love and duty,
But seeming so, for my particular end. . . .
But I will wear my heart upon my sleeve,
For doves to peck at: I am not what I am.
And so he continues throughout the play, sharing his inward thoughts and schemes with the audience, while playing the dutiful ancient with Othello.
Othello is caught up in the dilemma of appearance versus reality as well. He swallows, hook, line and sinker, all of the suggestions and false "evidence" that Iago presents him that Desdemona is unfaithful. The events of Acts III and IV surrounding the handkerchief are the ones that, in reality, are the most false, but appear to be the most damning.
These are merely a few of the examples of the themes of jealousy/revenge and appearance versus reality in the play Othello. For more on these and other themes, please follow the links below.