A: Washington, District of Columbia, United States
In 1880 John Shaw Billings, librarian of the Library of the Surgeon-General's Office (now the U.S. National Library of Medicine) began publication of the The Index-Catalogue of the Library of the Surgeon-General’s Office. This was the first "very large-scale" published subject index of any library, and the first truly comprehensive subject index of the published literature of any science.
Probably to obtain funding for the project, four years prior to the beginning of publication of the Index Catalogue Billings issued a Specimen Fasciculus of a Catalogue of the National Medical Library Under the Direction of the Surgeon-General, United States Army (Washington, 1876). Besides providing examples of his ambitious cataloguing plans, the fasciculus shows that Billings viewed the Library of the Surgeon General's Office as a national medical library, a designation that it would eventually receive in 1956.
Before online databases the Index-Catalogue became a landmark in the history of efforts to organize information and to make it searchable, and a primary general reference for the history of medicine and science. The fifith and final series was issued in 1961. The finished set of printed books contained "over 4.5 million. . . references to over 3.7 million bibliographic items. 2.5 million items are primarily journal articles; 250,000 items are monographs (books, pamphlets, and reports); approximately 300,000 items are dissertations (theses); and 16,000 are journal titles. Series 1 and Series 2 include portraits as separate citations but Series 3, 4, and 5 indicate portraits in descriptive notes for monographs and dissertations."
In 1952 the name of the library was changed to Armed Forces Medical Library; it became the National Library of Medicine in 1956. See S. J. Greenberg & P. E. Gallagher, "The great contribution: Index Medicus, Index-Catalogue, and IndexCat," J. Med. Libr. Assoc. 97 (2009) 108–113.
The Index-catalogue is available online from the U.S. National Library of Medicine at this link.