What sorts of ironies surround Iago in the first act of Othello?
If we take irony to be the discrepancy between appearance and reality, then certainly Iago is a character in whom irony abounds greatly in Act One. He takes great pains to appear to loyal confidante of Othello whilst actually working to act against him, informing Desdemona's father of Desdemona and Othello's elopement together. Note how he explains the way he must leave before Brabantio descends to Roderigo:
Farewell, for I must leave you.
It seems not meet, nor wholesome to my place,
To be produced, as, if I stay, I shall,
Against the Moor.
His whole identity is based on his hatred of "the Moor" and he takes great pains to appear to be loyal whilst plotting how to ruin his life. Note how in Act I scene 3, he says in a soliloquy:
He holds me well,
The better shall my purpose work on him.
Friendship and loyalty are just outward guises to allow him to advance his envious resentment against Othello.
In the first act of Othello, Iago practices a kind of verbal irony, which means that he says the opposite of what he truly means. While he detests Othello, he tells Roderigo in a sarcastic manner that he will follow Othello faithfully: "O, sir, content you; I follow him to serve my turn upon him: We cannot all be masters." He says he loves Othello in a moment of sarcasm while harboring only hate towards him.
Iago also character also contributes to dramatic irony, which is a situation in which the reality of something is not known to a character/characters. While Iago hates Othello, he tells Roderigo that he will head to Cyprus to feign loyalty to Othello:
Though I do hate him as I do hell-pains. Yet, for necessity of present life, I must show out a flag and sign of love."
While the audience is aware of Iago's hatred of Othello, "the moor," as Iago calls Othello, is not, making this a situation involving dramatic irony.