Hamlet

Hamlet was a play written by William Shakespeare. It was also the name of the titular prince of Denmark featured in the same play.

Genesis of the work
The Tenth Doctor and Martha Jones visited Shakespeare in 1599. They inspired Shakespeare to write about father-son relationships, which is the main theme of Hamlet. Shakespeare also mentioned the name of his deceased son, Hamnet. (TV: The Shakespeare Code)

The idea for Hamlet was first discussed at the court of Elizabeth I. The First Doctor, Ian Chesterton, Barbara Wright and Vicki Pallister used the Time-Space Visualiser to witness Shakespeare's initial rejection of Francis Bacon's thoughts on writing a play about Hamlet. They then saw Shakespeare appear to warm to the idea, once he'd left Bacon's presence. (TV: The Chase)

The First Doctor collaborated with Shakespeare between drafts one and two (PROSE: Byzantium!) and the Fourth Doctor claimed to have helped him write down the final draft of Hamlet after he sprained his wrist writing sonnets. This manuscript was acquired by Scaroth in the 20th century. (TV: City of Death, PROSE: The Stranger, The Writer, His Wife and the Mixed Metaphor)

Extraterrestrial references
The Monk believed that his meddling would enable Shakespeare to have Hamlet premiere on television. (TV: "Checkmate")

The Daleks quoted various lines from Hamlet while working on a time machine with Professor Osric. (AUDIO: The Time of the Daleks)

Behind the scenes

 * In The Chase, Bacon speaks of Hamlet as if he's common knowledge. Indeed, Shakespeare warms to the idea without ever having been told who Hamlet was. The direct implication is that Hamlet is a real person in the DWU. This marks a clear distinction between the DWU and our world. In the real world, Shakespeare never intended that Hamlet be taken as a biography. The character of Hamlet is an entire fiction. However, in the real world it is theorised Shakespeare wrote Hamlet in response to a less successful play about Hamlet. This would have been based on the story of Amleth, a legendary Danish Prince.
 * In The Mark of the Rani, the Sixth Doctor quotes a famous verse from the work ("There are more things in heaven and earth, than are dreamt of in your philosophy"), even if it is not explicitly attributed to it.

Doctor Who actors in Hamlet

 * In 1947, the first telecast version of the play also saw the television debut of actor Patrick Troughton in the role of Horatio.
 * A 1948 was the cinematic debut of Patrick Troughton in the role of the Player King. The film also had the first major film role for Peter Cushing who played Osric.
 * In 1980, Derek Jacobi played Hamlet, Lalla Ward played Ophelia, and Claire Bloom played Gertrude in a BBC TV production of the play, opposite Patrick Stewart as Claudius. The production also included one more Time Lord: Geoffrey Beevers was the murderer in the play within the play.
 * In 1996, Jacobi took the role of Claudius in a film that starred Kenneth Branagh as Hamlet. Brian Blessed, who had previously played Yrcanos in Mindwarp, played the ghost of King Hamlet. Richard Briers, who had played the Chief Caretaker in Paradise Towers, played Polonius. Nicholas Farrell, who would go on to play Brian Green in Children of Earth, played Horatio.
 * In 2002, Christopher Eccleston played the Hamlet at the West Yorkshire Playhouse.
 * In 2008, David Tennant took on the role of Hamlet in a Royal Shakespeare Company mounting of the play — opposite Stewart who once again played Claudius.