TARDIS library
The Doctor's TARDIS contained an extensive library.
It greatly varied in appearance. (COMIC: The Mark of Mandragora, PROSE: The Dimension Riders, TV: Journey to the Centre of the TARDIS)
For a time, the TARDIS control room contained a library, (TV: Doctor Who, COMIC: Endgame, AUDIO: Storm Warning) but, even during that time, the Doctor had a separate library as well. (PROSE: War of the Daleks, AUDIO: The Man Who Wasn't There)
The Master's TARDIS also contained a library. (PROSE: The Quantum Archangel)
Appearance
At one point, the walls of the library were covered in dark roundeled wood. (AUDIO: The Man Who Wasn't There)
Anji Kapoor thought that the library was "like some sort of optical illusion, with shelves disappearing into the far distance". (PROSE: Escape Velocity)
The Eleventh Doctor's TARDIS library was at least four floors high, with detailed architecture and vast amounts of bookshelves on each floor. The library was not modern in appearance but quite old-fashioned, with dark, walnut wood furnishings reminiscent of the styles of both medieval and victorian architecture. It contained several desks and lampshades, and the shelves appeared neatly organised and tidy. At least one shelving unit contained locked drawers. (TV: Journey to the Centre of the TARDIS)
History
Vicki Pallister used the library to research the United States of America. (PROSE: The Schoolboy's Story)
While the Fourth Doctor was not speaking with Leela after an argument, she found her way to the library, marking the walls along the hall. Leela decided to study a book of fairy tales to learn more about potential threats on Earth. When the Doctor discovered her, much to his surprise, she was reading "Jack and the Beanstalk" out loud from the book. He first checked the boot cupboard, the skulleries, both swimming pools and the lagoon. (AUDIO: White Ghosts)
Adric read every single book on mathematics in the entire library. (AUDIO: Zaltys)
According to one account, the TARDIS had at least two libraries during the time of the Fifth Doctor's travels with Erimem. (AUDIO: No Place Like Home)
On one occasion, the Sixth Doctor visited the library to check his address book and find the location of Vertipax. (PROSE: The Deal)
The Time Lords once send a message to the computer of library about the TIRU. (GAME: Doctor Who and the Mines of Terror)
Ace once sorted through the library. (AUDIO: Genocide Machine)
Bernice Summerfield once used the library to research the Shovoran dynasty. (PROSE: St Anthony's Fire)
When Anji Kapoor went into the TARDIS for the first time, she glanced into the library and was astounded by its size and messiness. (PROSE: Escape Velocity)
The Eighth Doctor and Charlotte Pollard once successfully sought out Pieter Montmarche: A Diary of Discovery in the library's children's literature section. (AUDIO: The Man Who Wasn't There)
When the Eighth Doctor, Lucie Miller, Susan, and Alex Campbell were attacked by a Blitzen fish during Christmas dinner inside the TARDIS, the library was among the rooms they were chased through. While there, they consulted Gauntlet's Bestiary of the Fourth Universe. (AUDIO: Relative Dimensions)
When the Eleventh Doctor crashed the TARDIS shortly after his regeneration, the swimming pool fell into the library. (TV: The Eleventh Hour)
While on the run from time zombies, Clara Oswald accidentally found the library and had a look through The History of the Time War. (TV: Journey to the Centre of the TARDIS)
While talking to Bill Potts, the Twelfth Doctor mentioned that the last time he went to the TARDIS library, Hattie was attacked by the 1986 Bash Street Kids annual. (PROSE: The Shining Man)
Collection
The library's books included Brave New World, (PROSE: The Wheel of Ice) Jane's Spaceships, (PROSE: War of the Daleks) Jane's Spacecraft of the Universe, Aladdin: The Script, Parachuting, A-Z of Planets, VNR The Collection, Timeview, The Time Machine, Collected Works of Beatrix Potter, The Baker's Dozen, Corpse, Vegetarian Cook, Vanity Fair, Freeman: Editorial Decision, The Early Years, a book on aerobics, (PROSE: The Deal) Every Gallifreyan Child's Pop-Up Book of Nasty Creatures From Other Dimensions, (PROSE: All-Consuming Fire) Robinson Crusoe, (PROSE: Heart of TARDIS) Wisden Almanack, (PROSE: Fear of the Dark) War and Peace, (PROSE: The Deal, AUDIO: Terror Firma) Baedeker's Galactic Guide, Bajazet Magna to Bali, (PROSE: Cat's Cradle: Time's Crucible) The Wonderful Wizard of Oz, The I-Spy Book of British Birds, Can you forgive her?, You Only Live Twice, Frankenstein, (AUDIO: Storm Warning, Zagreus) Pieter Montmarche: A Diary of Discovery, The Little Book of Starships, (AUDIO: The Man Who Wasn't There), the only signed copy of The Quarry in the universe (PROSE: Keeping up with the Joneses) and a signed copy of Reminiscences of the Peculiar by George Litefoot. (AUDIO: The Carrionite Curse)
Some of the library's history books included A History of the Varaxil Hegemony, (AUDIO: The Witch from the Well) Histories of the Dalek Imperium, (PROSE: Keeping up with the Joneses) The History of the Time War, (TV: Journey to the Centre of the TARDIS) A Brief History of Time, (PROSE: Fear of the Dark) and Fashion Through the Ages. (PROSE: The Deal)
The Demonology and Witchcraft section contained books by an author named Rowling. (AUDIO: The Carrionite Curse)
Books kept in the library which were of personal significance to the Doctor included a signed copy of The Murder of Roger Ackroyd gifted to him by Gemma and Samson Griffin (AUDIO: Terror Firma, Terror Firma) and his Five Hundred Year Diary. (PROSE: The Deal, AUDIO: The Young Lions)
He had several books by writers such as Capek, Capote, (AUDIO: Zagreus, PROSE: The Blood Cell) Carroll, (AUDIO: Zagreus) and Shakespeare. (PROSE: The Deal, The Dimension Riders)
The contents of the library were not limited to books. It also contained a stack of 45 singles and EPs by Billy Fury, Adam Faith and the Beatles, (PROSE: Cat's Cradle: Time's Crucible) the sentient liquid Encyclopedia Gallifreya, (TV: Journey to the Centre of the TARDIS; PROSE: Citation Needed) and diskettes containing the complete works of the 21st century environmentalists. (PROSE: The Dimension Riders)
The section of the library devoted to children's literature was "ridiculously small". (AUDIO: The Man Who Wasn't There)
Behind the scenes
The incomplete television story Lost in the Dark Dimension would have featured the TARDIS library for a significant portion of the story. Set in an alternate timeline where the Fourth Doctor never regenerated and the TARDIS was mostly destroyed, the library would have been the last fragment of the ship remaining, camouflaged as a small church.
For some of the shots of the Eleventh Doctor's TARDIS library, Cardiff Castle's library was used. This vast library was built on the site of an old medieval hall during the 1800s, giving it a mixture of design influences from different periods of time.