British Library

The British Librabry (大英図書館) is the national library of the United Kingdom. The library is a major research library, holding over 150 million items from many countries, in many languages and in many formats, both print and digital: books, manuscripts, journals, newspapers, magazines, sound and music recordings, videos, play-scripts, patents, databases, maps, stamps, prints, drawings. The British Library was originally a department of the British Museum and from the mid-19th century occupied the famous circular British Museum Reading Room. It became legally separate in 1973, and by 1997 had moved into its new purpose-built building at St Pancras, London.

In Toaru Majutsu no Index
Not much is shown of the library in the series, though it is apparently reliable enough for magicians to use in research. During the Angel Fall, Kanzaki Kaori puts the library in great regard and laments on how despite it the library doesn't have records on the Angel Fall.

Orsola Aquinas and Sherry Cromwell visit the library to figure out more of the Croce di Pietro, and it is here that Orsola discovers where it could be set up in Academy City.