Library

Libraries, or athenæums (PROSE: Against Nature) were places where books collected. Some libraries were public, while others were contained to private homes, for access from within more solitary spaces.

TARDIS libraries
Both the Doctor's TARDIS and the Master's TARDIS had libraries. (PROSE: War of the Daleks, All-Consuming Fire, The Dimension Riders, The Quantum Archangel, TV: Journey to the Centre of the TARDIS) The interior of Professor Chronotis' TARDIS was a library. (TV: Shada)

These libraries existed outside of time, always travelling alongside their respective pilots to faraway times and places. Some of these TARDIS libraries involved sentient books, like the Encyclopaedia Gallifreya, which worked to record the Doctor's many journeys, from deep within their TARDIS. (PROSE: Citation Needed) Companions who found their way here were prone to discovering secrets, especially along the Doctor's time stream, details which were often relevant to the ongoing adventure. (TV: Journey to the Centre of the TARDIS, AUDIO: Relative Dimensions et al.)

Late returns
As a time traveller, the Doctor had library cards under different identities, which could be confusing for others, (TV: The Vampires of Venice) and in different times, different places. In amongst the chaos of their lives, the Time Lord often brought books with them well beyond their due date, under the assumption that they could always go back and fix this problem.

In practice, the Doctor was known for "evading library fines", and was sometimes brought under charge for these violations, alongside more serious charges, like "planetary demolition". (TV: The Infinite Quest)

On Earth
The Library of St John the Beheaded was owned by the Catholic Church and located in London. It had a large collection of occult literature and forbidden texts, including lost works by Plato, Aristophanes and Shakespeare, as well as specific works like the journal of Redvers Fenn-Cooper, (PROSE: All-Consuming Fire) The Gnostic Apocrypha of Nostradamus, (PROSE: Millennial Rites) and Love's Labour's Won. (PROSE: The Empire of Glass)

Bruce Lee kept a library in his home, where he collected books on philosophy, history and martial arts. (COMIC: The White Dragon)

There was a library in the Powell Estate. (PROSE: Winner Takes All)

The Twelfth Doctor, Clara and Rigsy met in front of the Great British Library. (TV: Face the Raven)

The Terrance Dicks Library was located in St Luke's University. (COMIC: The Lost Dimension)

Across the universe
The Labyrinth of Kerykeion had the largest collection of human books outside of Earth in the 27th century. (AUDIO: Timeless Passages)

The Library on Kar-Charrat was known as being one of the wonders of the universe. It contained knowledge from every civilised planet in the universe. Even so, the librarians never liked to advertise its presence and so it was rarely visited and the books were practically untouched. (AUDIO:  The Genocide Machine)

The Library, which was built during the 50th century, covered an entire planet and contained "every book ever written". (TV: Silence in the Library)