Shadow of Darkness
Kate behaves like a shrew and has no marriage prospects.
According to Booker, Katherine's shrewishness places her in a "dark" state. Not only does she behave badly, she fails to recognize that her shrewish ways are the cause of her social isolation and unhappiness. No man will marry Kate and she claims not to be interested in marriage at all. Kate's state of "darkness" also throws a "shadow" over the other characters in the play and causes them to be unhappy as well. Aside from her obnoxious behavior, Kate's shrewishness is a problem because, as long as she's unmarried, her sister Bianca cannot marry and find happiness either.
Pressure of Darkness
Petruchio and Kate are engaged and married and Petruchio attempts to "soften" Kate's wild behavior.
Once engaged and then married, Petruchio attempts to bring Kate out of her state of darkness by holding up a figurative mirror to her behavior. Kate resists Petruchio's efforts to bring her into a state of self-awareness, which causes even more misery for Kate and others (especially Petruchio's servants, who bear the brunt of Petruchio's erratic behavior). Kate's life is a living nightmare, as she is starved, deprived of sleep, and intimidated for not behaving like a dutiful wife.
Everything Comes to Light
On the road to Padua, Kate finally breaks and becomes an obedient wife to Petruchio.
Finally, Kate sees the light and recognizes that her bad behavior has caused so much unhappiness and misery. Kate agrees to go along with Petruchio when he insists that the sun is the moon and an old man on the road is a young virgin. This signals that Kate's attitude and shrewish behavior have changed and she is miraculously transformed into an obedient, loving wife. Kat and Petruchio attend Bianca's wedding banquet, where she delivers a long speech about a wife's proper obedience to her husband. The situation has been "miraculously transformed." Petruchio, the "hero" has softened Kate into a dutiful bride. After Kate's speech, they exit the stage in a state of unity and love.