Gallifreyan (language)

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)

The written form of Old High Gallifreyan resembled, to human eyes, a mixture of Greek letters and mathematical symbols.

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 δ³Σx², 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)

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 Hieratic-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 Doctor's TARDIS output screens in "coral desktop theme" mode 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. (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)

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 τηεψ ωερε αλλ ωεαρινγ εψεπατχηεσ." The passage doesn't actually mean anything in Greek, but if transliterated letter-by-letter to English in the Symbol font the passage becomes "And I turned around and they were all wearing eyepatches," a sly reference to the infamous Eyepatch Story.