What are the gender roles in Shakespeare's time?
When you talk about gender roles in Shakespeare's day, you can't limit the discussion to male and female. You need to take social status and class into consideration.
Of course, the people with the least restrictions were the royalty, but even they were expected to fall into certain molds. If you've seen the movie Elizabeth, you know how she was hounded to get married, not just to provide an heir but because they just weren't used to being governed by a woman.
The nobility is the next rung down. Other classes that need to be taken into account are the gentry, the working class, and the poor.
Women of noble birth or of the gentry class (the growing middle class merchants) may have been educated. The nobility could at least read and were trained in needlework. They were often used as bargaining chips in making alliances or business mergers through marriage. No women were allowed to vote.
The working class woman was not allowed to enter a profession, such as law or medicine, but she could be a domestic servant or assist her husband in his trade.
Poor women had to make due in whatever way they could.
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