Rare Book and Manuscript Library
The Rare Book and Manuscript Library contains a lot of old shit (e.g. there are documents that are literally 4,000 years old, including but not limited to "cuneiform tablets, papyri, and Coptic ostraca"). It also contains "literary manuscripts from the 14th century [and] the papers of authors Herman Wouk and Erica Jong", as well as the papers of the Carnegie Endowment for International Peace, Random House, NGOs such as Human Rights Watch and Amnesty International-USA. Some of the University Archives are also located here.
The library is located within the bowels of Butler Library, and is guarded by very protective librarians with a deep suspicion of undergraduates. On the plus side, it's totally climate controlled and will be a very pleasant temperature no matter how it feels outside.
