The induction is a great success and importance to the play because it gives many hints and clues to what the play proper is going to be about, it creates a comedic theme, which is created by the language used by Christopher Sly, it introduces many themes that link to the play proper i.e. deception and illusion and it summaries the play as a whole. .
Obviously the play proper can stand on its own, but the story of the Lords practical joke on Christopher Sly does reinforce one of the main themes in the main play. Sly's story dramatises the idea that a persons environment and the way he is treated by others determines his behaviour, which is an idea that Katherine's story in the main play also illustrates.
Deception is one of the main themes in which we are introduced to in the induction and then is continued throughout the duration of the main play. For example the Lord thrusts Sly into a play-acting world and portrays his new role, as coming into being through no will of his own. The Lord huntsman emphasises this when asked if Sly would fall for the deception and forget himself "Believe me Lord, I think he cannot choose". The huntsman's words could equally apply to Katherine. .
Katherine is forced to play a part of a "perfect" wife which is a social role which she initially rejects. The implication that Katherine like Sly "Cannot choose" suggests that she is as much a plaything of Pertruccio as Sly is of the lord. .
Another theme is illusion and reality. The main play is an illusion, as it is a play within a play. The reality that occurs is that Sly believes he is a Lord "for he is nothing but a mighty Lord" and Page pretending to be Sly's wife, this is also an illusion because he is actually a man, this adds to the humour of the play. .
In scene two of the induction Page and Sly are having a conversation when Page states "my husband and my lord, my lord and husband, I am your wife in all obedience" which we presume he means that they will get married and his wife will be obedient.