William Shakespeare

William Shakespeare won renown as the greatest poet and playwright in the history of England and one of the greatest in human history. He also had numerous encounters with the Doctor and was attracted to Martha Jones (DW: The Shakespeare Code). One of his plays, Hamlet, was written with help from the Doctor (DW: City of Death), and another, Troilus and Cressida would, unknown to Shakespeare, be actually based upon the later life of the First Doctor's companion, Vicki, who adopted the identity of Cressida. (DW: The Myth Makers)

Encounters with the Doctor
The Eighth Doctor and Charley Pollard met a young Will Shakespeare who had been taken out of his rightful time (1572) by Viola Learman and brought to New Britain in the early 21st century. Will Shakespeare may have learnt about his own plays from Mariah Learman's library. Due to the traumatic nature of these and later events (BFA: Zagreus),his life may have been changed retroactively to explain any discrepancies. (BFA: The Time of the Daleks)

In 1597, The Doctor shared a drink with an older Shakespeare; he later stowed away in the Doctor's TARDIS and began to attempt to influence the reign of King Richard III of England to more closely resemble the account in his play Richard III. This adventure ended with Shakespeare being killed in King Richard III's place at the Battle of Bosworth in 1485, and Richard returning to 1597 to take Shakespeare's identity and place in history. It is heavily implied that the CIA fixed the events of this story, which may explain how Shakespeare later did not recognise the Doctor. (BFA: The Kingmaker)

Some time in the same decade, The Ninth Doctor and Rose Tyler encountered Shakespeare. At the Doctor's request, Rose agreed to distract Shakespeare "with a hey nonny nonny." He dismissed an attempt by Shadeys to destroy the Earth as a trick-show, and did not let it interfere with his future career. The meeting between the Doctor and Shakespeare was fleeting however, and may not have made much of an impact on his life as other meetings subsequently did. (DWM: A Groatsworth of Wit)

In 1599, The Tenth Doctor encountered Shakespeare when the witch-like Carrionites wanted the wordsmith to complete the play Love's Labour's Won to free the rest of their kind. With the help of the Doctor and Martha Jones, the three Carrionites and their sisters were banished back into the Deep Darkness. During this encounter, Shakespeare developed an attraction to the Doctor and Martha, whom he addressed as his "Dark Lady" (DW: The Shakespeare Code). He did not give any indication that he had ever met the Doctor prior to this point in his life, though it is likely that he did not remember previous encounters (as in DWM: A Groatsworth of Wit) or had been made to forget the events (as in BFA: The Kingmaker).

Via the Time-Space Visualiser, the First Doctor and his companions watched William Shakespeare in conversation with Queen Elizabeth I. (DW: The Chase) Years later, the Fourth Doctor helped Shakespeare transcribe Hamlet as Shakespeare had sprained his wrist writing sonnets. The Doctor claimed that he had warned Shakespeare that Hamlet's line "to take arms against a sea of troubles" was a mixed metaphor, but Shakespeare would not listen. (DW: City of Death)

In 1609, Shakespeare, acting as an agent of the Crown, encountered the Doctor, Irving Braxiatel, and Galileo Galilei, and was reunited with Christopher Marlowe, whom he thought was dead. The Doctor forcibly made Shakespeare take a Retcon-like drug to erase his memory of the events he had witnessed. (MA: The Empire of Glass)
 * It is unknown, but possible that this affected Shakespeare's recollection of his other encounters with the Doctor.

Personality
Shakespeare was notable for being one of the few humans who, without receiving any known sort of psychic training, was not fooled by the Doctor's psychic paper. The Doctor was very impressed by this fact and applauded him, stating it was proof that he is a genius. (DW: The Shakespeare Code)

Behind the scenes

 * In The Shakespeare Code, the Tenth Doctor acts as though he's never met Shakespeare before, despite the Fourth Doctor indicating in City of Death that he knew Shakespeare well enough to help him write Hamlet. Reportedly a line of dialogue was written for the later episode to explain this, but the line was cut.
 * From the Bard's perspective, though, this is not a contradiction, as Hamlet was believed to be written between 1599 and 1601. So Shakespeare likely met whichever Doctor helped him transcribe Hamlet after the events of The Shakespeare Code, in Shakespeare's own personal timeline.


 * Shakespeare would still have met the Doctor several times before The Shakespeare Code based on other episodes in the series, and a few more if the novels and audio dramas are counted. But of course Shakespeare would not recognize the Doctor from appearance since the Doctor's face and body keep changing. Still, one wonders why the Bard would not have commented on having met others who referred to themselves simply as "The Doctor." Perhaps the past meetings are what help Shakespeare deduce the truth about the Doctor and Martha.


 * During The Shakespeare Code there is a moment when the Doctor notices Shakespeare is flirting with him after just having done so with Martha. The Doctor says, "Come on, we can all have a good flirt later!" [in reference to them needing to stop the Carrionites]. Shakespeare responds, "Is that a promise, Doctor?" The Doctor muses, mostly to himself, "Fifty-seven academics just punched the air." This is a reference to the idea that most of Shakespeare's sonnets, including Sonnet 18, are believed by some Shakespearean academics to be addressed to a man, and there is a sizable body of scholarship on Shakespeare's sexuality.


 * The revelation in The Kingmaker that the original Shakespeare left his time in 1597 and was killed in 1485, only for Richard III to return to 1597 and take the prematurely deceased writer's place, has not been acknowledged or addressed by in-universe portrayals of Shakespeare post-1597.