The comedy opens with music being played to remind the duke of Olivia; the first scene discusses the lady's charms; and she is mentioned in the second scene as having lost a brother. Viola feels an instant empathy with a person mourning a lost brother since she herself believes that her brother is also drowned. In the third scene, Olivia's house is the setting, and in the fourth scene, Olivia is again the central subject of discussion. Thus, we hear a great deal about this important lady before we actually meet her.
At first, Olivia seems to be the emotional counterpart for the duke; he is a melancholy parallel for Olivia, and Olivia has sworn to abjure the world for seven years to mourn for her dead brother, an act of extreme sentimental melancholy. Olivia is also the opposite of Viola in many ways. While Olivia is attracted to her opposite (Viola in the guise of Cesario), Viola will be attracted to her opposite, Duke Orsino.
Other than the melodramatic pose that Olivia is assuming at the beginning of the play (we know it to be a pose because she is willing to immediately discard it in order to flirt with Cesario), Olivia is presented as being essentially an intelligent woman with a number of good qualities. Her intelligence is constantly seen in the many household matters that she has to attend to. She has to contend with her drunken uncle, Sir Toby Belch, and when Malvolio presents himself in his mad garb, she feels compassion for her foolish steward. Yet, earler when Feste made fun of Malvolio, the over-serious steward, Olivia was fully capable of appreciating the clown's wit.
The single quality that characterizes Olivia best is perhaps her impetuous love and her assertion of it. She is much more aggressive in the pursuit of her love than is Duke Orsino in his pursuit of Olivia. While she recognizes the duke's good qualities and acknowledges them, she is adamant in her refusals, and, thus, it is part of the comedy that the lady who has no sympathy for the duke falls so irrationally in love with a young girl disguised as a young boy. When she discovers that she has actually married young Sebastian, Viola's twin, she quickly transfers her love to him, just as Duke Orsino is able to transfer his love to Viola.