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What was Shakespeare's motivation for writing Hamlet?
The plague had caused the closing of the theatres and he wanted to gain back lost money upon their reopening.
He thought that Hamlet's story needed to be told so that his good name could be cleared in history.
Queen Elizabeth was aging with no heirs and England was questioning who would succeed to the throne, and succession is a main idea in Hamlet.
Shakespeare's twins had just been born. Since he named the boy Hamnet, he wanted to pen a play in his son's honor.