One of William Shakespeare’s earliest plays, The Taming of the Shrew was probably written in about 1590-91, and centres on one of the evergreen themes for stories and plays. It has proved popular on the stage, in various adaptations including Cole Porter’s famous musical Kiss Me, Kate, and has been painted frequently as well.
The play starts with an Induction, in which a tinker Sly is thrown out of a tavern, put to bed, and when he awakes is told that he’s a lord who has suffered from delusions for years. Sly is duped by a page dressed as a woman, and agrees to watch a troupe of players perform a comedy, the cue for the play to start.

Henry Corbould’s painting of Hostess and Sly, shown in this engraving from 1825-40, sets the scene for the opening Induction, with Sly being thrown out of the tavern.
A student, Lucentio, arrives in Padua where he falls in love with Bianca. Her father tells him that she can only be courted when her older sister Katherine has been married, and will remain at home until then. Bianca’s other suitors decide to look for a match for the disdainful Katherine, but Lucentio can’t wait, and decides to pose as a tutor for her, leaving his servant Tranio to take his place.

Stanisław Wyspiański’s pastel Portrait of Honoraty Leszczyńskiej in the role of Katherine was painted in 1894.
Petruchio arrives from Verona, and despite Katherine’s reputation as a shrew, decides to woo her for her dowry. He recommends his friend Hortensio to be Bianca’s music teacher, and Bianca’s other two suitors agree to fund Petruchio’s suit for Katherine as her marriage will enable them to court her younger sister.

Benjamin van der Gucht’s portrait of Henry Woodward as Petruchio shows the actor in a version of the play by Garrick, and was painted in 1773-74.

Ivan Kramskoi’s portrait of The Actor A.P.Lensky as Petruchio was painted in 1883.
Bianca is being interrogated by her older sister about her suitors when their father arrives and splits them up. Petruchio and the suitors return from the tavern, and once he has confirmed the size of her dowry, Petruchio puts himself forward as her suitor. He then offers his friend Hortensio, disguised as Licio, as Bianca’s music teacher, and one of Bianca’s suitors offers Lucentio, disguised as Cambio, as her tutor. They are accepted, but Hortensio quickly returns when Katherine breaks a lute over his head. He is then sent to Bianca.

Louis Rhead’s wonderful ink drawing of Katherine Breaking a Lute Over Hortensio’s Head was made in about 1918 for an illustration in Lamb’s Tales.

James Dromgole Linton’s watercolour double portrait of Katherine and Petruchio was painted in the middle of the nineteenth century.
Petruchio’s meeting with Katherine proves difficult because of her contempt for him. He tells her father that she has agreed to marry him the following Sunday, to which her father agrees, despite her protests. Bianca’s false tutors then bargain for her hand, with Lucentio’s servant winning by promising all the wealth of his master’s father. This Bianca’s father accepts, subject to confirmation with the father.
Bianca’s two suitors, both acting as her tutors, declare their true identities and objectives to her. When she favours Lucentio, Hortensio is disgusted.
Petruchio arrives late and badly dressed for his wedding to Katherine. After the church ceremony, her father tells Bianca’s suitors of his bad behaviour, and the groom drags his bride away before their wedding breakfast.

Francis Wheatley’s painting of Taming of the Shrew, Act III, Scene II from 1795 is shown in this engraving, which appears to have been made to accompany Boydell’s Shakespeare Gallery, and shows Petruchio dragging Katherine away from their wedding.

Carl Gehrts’s richly inventive watercolour of Petruccio’s Wedding from 1885 captures the atmosphere of a wedding breakfast, although Petruchio doesn’t look to be dragging his bride away from it.
Later, when the couple arrive at Petruchio’s country house, the groom abuses the servants and sends Katherine to bed alone without having anything to eat. He explains to the audience that he intends to break her spirit, and asks whether anyone knows of a better way to tame a shrew.

Washington Allston’s painting of Katherine and Petruchio from 1809 shows the bride looking away in disdain, although it’s not clear which of the two men standing is intended to be Petruchio.

Robert Braithwaite Martineau’s painting of the couple, in Katherine and Petruchio (1855), shows her disdain in the face of his control over the door behind him.
Hortensio takes Lucentio’s servant to watch Bianca and Lucentio courting, and immediately Hortensio abandons his suit for her and goes to court a wealthy widow instead. Bianca, Lucentio and his servant then work out how to obtain her father’s agreement using a stand-in for Lucentio’s father to commit the wealth of his real father. The servant then tricks a passer-by into playing that role.
Petruchio’s servant refuses to let Katherine eat, and helps his master reject her new clothes she was going to wear when she visited her father. Petruchio abuses the haberdasher and tailor, and insists she will only go to her father when she’s completely obedient to him.

Charles Robert Leslie’s scene of Catherine and Petruchio (1832) shows her seated at the left, as her new husband dismisses the haberdasher and tailor bringing her new clothes, including an enormous green hat box held by an anxious tradesman.

Michael William Sharp’s account of Petruchio and the Tailor from 1835 shows Petruchio with his sword drawn, as he argues with the tailor, who is holding up the original order as he tries to defend his work.
Lucentio’s servant introduces the stand-in for his master’s father to Bianca’s father, and they convince the latter to sign the marriage settlement later, after supper. While they do that, Lucentio is advised to marry Bianca in private.
As Katherine is on her way to visit her father, Petruchio has her call the sun the moon. When they arrive, Lucentio’s real father is there, and is surprised to learn of his son’s forthcoming marriage.
Lucentio and Bianca hurry to their secret wedding, where they meet Katherine and Petruchio with Lucentio’s real father. The stand-in then insists that he is really Lucentio’s father. He is followed by Lucentio’s servant, who is dressed as his master, causing the real father to believe that his son has been murdered by his servants. Bianca’s father tries to have Lucentio’s real father imprisoned for being an imposter. Lucentio and Bianca reappear after their marriage ceremony has been completed, driving away the servants and the stand-in. Lucentio reveals his deception, and Petruchio persuades Katherine to kiss him in the street.
Both couples, their fathers, and servants gather at the banquet to celebrate the weddings of Lucentio to Bianca, and Hortensio to the rich widow. When Katherine, Bianca and the widow leave the room, their new husbands bet twenty crowns that their wife will be the most obedient to return when they call them. Although both Bianca and the widow refuse, Katherine comes promptly, goes to fetch the other two, then tells them at length about the wife’s duty of obedience. To Petruchio’s winnings, the father of Bianca and Katherine adds another twenty thousand crowns.
With the play ended, Sly is asleep. He is returned to his old clothes and the place that he originally fell asleep. He is awakened at dawn, and told that he had a dream in which he learned how to tame a shrew, and can have no fear of going home to his wife.
References
Wikipedia on Shakespeare’s play.
Full text at Project Gutenberg.
Michael Dobson and Stanley Wells (eds) (2015) The Oxford Companion to Shakespeare, 2nd edn, Oxford UP. ISBN 978 0 19 870873 5.