Gallifreyan (language)

Gallifreyan was a Gallifreyan language used by the Time Lords. There were several forms of written Gallifreyan. By the time of the Doctor, the archaic Old High Gallifreyan language used in the days of Rassilon had changed considerably. (TV: The Five Doctors) TARDISes' translation circuits translated neither Old High Gallifreyan nor Gallifreyan written in the Doctor's time. (PROSE: The Price of Paradise, TV: The Time of Angels, A Good Man Goes to War)

Old High Gallifreyan
Old High Gallifreyan was the ancient language of the Time Lords. It was not known by many by the Doctor's era. (TV: The Five Doctors) When speaking of the immense power of his ancestors, the Eleventh Doctor stated that Old High Gallifreyan once possessed the power to raise empires and destroy gods. (TV: The Time of Angels) He later stated that Old High Gallifreyan had tenses that aided in speaking about time travel. (PROSE: Borrowed Time)

The written form of Old High Gallifreyan resembled, to human eyes, a mixture of Greek letters and mathematical symbols. (TV: The Five Doctors) Marnal manipulated his bottle universe with controls labelled in a language that looked like Greek, but he clarified that it was the "Gallifreyan omegabet." (PROSE: The Gallifrey Chronicles)

Inside the Tomb of Rassilon in the Death Zone on Gallifrey, an old rhyme was written in "Old High Gallifreyan," which explained the outcome of the "Game of Rassilon". (TV: The Five Doctors)
 * This text included the letters ∂³∑x², which was given as the Doctor's name in the 1972 behind-the-scenes book The Making of Doctor Who by Terrance Dicks and Malcolm Hulke.

Within the Doctor's rooms on the Gallifrey of one universe, there was a painting of a woman holding a scroll with the words "Death is but a door" written in High Gallifreyan. (PROSE: The Infinity Doctors)

The First Doctor wrote his Five Hundred Year Diary in High Gallifreyan to make sure no one else could read it. (PROSE: The Power of the Daleks)

Susan Foreman wrote the Doctor's real name on the wrapping paper of a hypercube intended for him. (PROSE: Ghost of Christmas Past)

River Song could write in Old High Gallifreyan. (TV: The Time of Angels)

The word "valeyard" was said to mean "learned court prosecutor". (TV: The Trial of a Time Lord)

"Mi'en Kalarash" translated as "Blue Fire". (AUDIO: House of Blue Fire)

The Fifth Doctor once spoke a sentence in Gallifreyan to Patience, who recognised it. To Adric's ears the speech sounded musical, like a nursery rhyme. (PROSE: Cold Fusion)

Modern Gallifreyan
While Old High Gallifreyan was the original language of the Time Lords, it had evolved into a different form by the time of the Doctor. (TV: The Five Doctors)

Two Time Lords looked at an archive of information on the Third Doctor, which displayed a photo and writing in modern Gallifreyan. (TV: Colony in Space)

A vaguely -looking script, in a letter written by the Fourth Doctor to warn the High Council of an assassination, was in modern Gallifreyan. (TV: The Deadly Assassin)

The Seventh Doctor left a calling card for the Supreme Dalek in a script other than English. It appeared to include the Greek characters Theta Sigma (TV: Remembrance of the Daleks), which had been an old nickname of the Doctor's. (TV: The Armageddon Factor)

Circular Gallifreyan
Gallifreyan could also be written using interlocking circles, hexagons and lines, at least by the time of the Last Great Time War. (TV: The End of Time)

A complex system of interlocking circles was used by the scanner screens in the Ninth Doctor's TARDIS and was seen in the notes that the Doctor scattered around the console room. (TV: Rose onwards)

Simpler handwritten circles appeared on the Betamax tape used by the Tenth Doctor to trap the Wire. The circular text, since scribbled over, presumably stated the tape's contents. (TV: The Idiot's Lantern)

Captain Jack Harkness's office in the Torchwood Hub had windows with circular Gallifreyan engraved on them. (TV: Everything Changes - Children of Earth: Day One) However, these were likely destroyed when a bomb was implanted in him without his knowledge and used to blow up the Hub once he was inside. (TV: Children of Earth: Day One)

The Visionary wrote interlocking circles, which Rassilon and the other Time Lords could understand. One of the words was "Earth." (TV: The End of Time)

The envelope from the Eleventh Doctor inviting River Song to Lake Silencio, and a page from the 1,103-year-old Eleventh Doctor's TARDIS diary, were written in Circular Gallifreyan. (TV: The Impossible Astronaut)

Text in circular Gallifreyan was seen carved into the Doctor's cot. (TV: A Good Man Goes to War)

A blue fire extinguisher that the Eleventh Doctor used on the TARDIS was marked in silver Circular Gallifreyan. (TV: The Angels Take Manhattan)

The Eleventh Doctor's second TARDIS control room design featured circular Gallifreyan symbols on rotating sections above the main console and time rotor. (TV: The Snowmen)

The Whisper Men showed Clarence DeMarco a map that he had to memorise in Circular Gallifreyan that they demanded he give to Madame Vastra. (HOMEVID: Clarence and the Whispermen) These were space-time coordinates which led to Trenzalore, the final resting place of the Doctor following the Siege of Trenzalore. (TV: The Name of the Doctor)

Circular Gallifreyan writing was written on the sides of the TARDIS exterior after it had entered siege mode. (TV: Flatline)

The blind Twelfth Doctor employed a reading aid which had circular Gallifreyan script on it. (TV: Extremis)

Behind the scenes

 * The number system in circular Gallifreyan, as seen in the chapter headings of the New Series Adventures, was in base seven.
 * The Gallifreyan spoken by the Doctor in Cold Fusion is represented in the text by Greek type: "Ανδ Ι τυρνεδ αρουνδ ανδ τηευ ςερε αλλ ςεαρινγ ευεπατψηεσ." The passage doesn't actually mean anything in Greek, but if transliterated letter-by-letter to English in the the passage becomes "And I turned around and they were all wearing eyepatches," a sly reference to the infamous Eyepatch Story.
 * While none of the Gallifreyan languages used in the show have been given translations, numerous translatable fan made versions have been made.
 * A version of Circular Gallifreyan was created by Doctor Who fan Lorna Sherman. Despite being fan made, it has made its way onto official Doctor Who merchandise, including one symbol on Arianna Florean's Cover D of The Tragical History Tour: Part 2. The Gallifreyan was created by DeviantArt user phantoms-siren, and is the iconic Sherlock Holmes quote, "When you have eliminated the impossible, whatever remains, however improbable, must be the truth!"