How does The Tempest explore and expose the anxieties about travel, exploration and colonization in the seventeenth century?
This is of course a pressing concern for the action in this marvellous play. We need to remember that this play was written against a backdrop of wide-scale European colonial expansion. This had resulted in a whole host of stories and strange tales of different worlds and cultures that entertained and terrified the audiences of Europe in equal measure. The majority of people concluded that Europeans had an absolute right to travel to other cultures and impose their culture and plunder. However, a few dissenting voices were concerned that the "civilisation" that Europeans offered might not be entirely beneficial to the indigenous populations of these places.
We can see this tension developed in this play. You would do well to pay attention to more recent productions of this play that cast Caliban in a far more sympathetic light as a wronged colonial subject who has had his territory and power taken away from him and is kept in conditions that resemble near-slavery. However, as with all of Shakespeare's plays, it is important to decide how you would stage the relationship both between Prospero and Caliban, and also Prospero and Ariel. How you answer that question will reflect your own thoughts about the theme of colonialism in this play.