Short answers, pulled from the story.
The Tempest was probably written between late 1610 and mid-1611. It is considered one of the last plays Shakespeare wrote alone, though it was followed by collaborations with John Fletcher on Henry VIII, Cardenio, and The Two Noble Kinsmen.
The Tempest explores magic, betrayal, revenge, forgiveness, and family. It also examines colonialism through Prospero's control of Caliban and Ariel, questions of chastity and dynastic marriage, and the nature of theatrical illusion, with Prospero's art explicitly linked to the stage itself.
The central character is Prospero, the rightful Duke of Milan, who lives on a remote island with his daughter Miranda. His two servants are Ariel, an airy spirit, and Caliban, son of the deceased witch Sycorax. The shipwreck survivors include Alonso, King of Naples; his son Ferdinand; his brother Sebastian; and Prospero's treacherous brother Antonio.
The Tempest has no single obvious source. William Strachey's eyewitness account of the 1609 wreck of the Sea Venture off Bermuda is considered a primary source for the opening storm. Gonzalo's ideal society echoes Montaigne's essay "Of the Canibales" in John Florio's 1603 English translation. Prospero's farewell to magic draws on Medea's invocation in Ovid's Metamorphoses.
Beginning around 1950 with Octave Mannoni's Psychology of Colonization, postcolonial critics read Prospero as a coloniser who seizes the island and enslaves its inhabitants Caliban and Ariel. Caliban's line "This island's mine... which thou tak'st from me" became a rallying cry for African and Caribbean intellectuals in the 1960s and 1970s. Writers including Aimé Césaire and Roberto Fernandez Retamar produced postcolonial adaptations setting the play in Martinique and Cuba respectively.
The earliest recorded performance was on the 1st of November 1611 at Whitehall Palace before King James I. From the Restoration until the mid-19th century, heavily adapted versions dominated the stage; William Charles Macready's 1838 production was the first to restore Shakespeare's original text to primacy. By the end of 2005, BBC Radio had aired 21 productions of The Tempest, more than any other Shakespeare play.