Shakespeare’s The Tempest is a very late play by Shakespeare, among those often referred to as his ‘problem’ plays; they are problematic in that they avoid easy categorisation into comedy or tragedy. They are also sometimes know as romances. Prospero is the key figure, a magician who uses chaos to restore order, but who can also be read as a domineering colonist of the island on which he is marooned. His speeches about power, imagination and books have led many scholars to equate him with Shakespeare himself, acknowledging the final scenes of his play writing career.
As a quick introduction, here’s the BBC animated version:
Emma Smith, from Oxford University, is always worth reading or listening to. Her lectures on Shakespeare are available online, and here is her talk about The Tempest.
You might also like to explore the Royal Shakespeare Company’s archive on the play, with information, summaries and production history.