It houses one of the few remaining libraries in Gilead that remain after the enthusiastic book-burnings across Gilead: Hildegard Library. Saint Hildegard was a German Benedictine abbess in the Middle Ages, who is considered to be the founder of scientific natural history in Germany. Aunt Lydia has a private sanctum inside. The library holds locked-up Bibles, as well as the Bloodlines Genealogical Archives - where Aunts hold information about the true biological parents of children in Gilead, as to prevent incest and the resulting Unbabies. There is also a Forbidden World Literature section. Lydia keeps a private collection of books, including Jane Eyre, Anna Karenina, Tess of the d'Urbevilles, Paradise Lost, and Lives of Girls and Women.
The Schlafly Café is the eating hall of Ardua Hall. It refers to Phyllis Schlafly, anti-feminist and staunch conservative lawyer and activist (and possibly to her son Andrew, founder of the conervative-biased online wiki, Conservapedia - referencing the Aunt's own censorship and strict records).
It houses the statues of the four founding Aunts of Gilead: Lydia, Elizabeth, Helena, and Vidala. Aunt Lydia's statue was commissioned 9 years before the beginning of The Testaments. Visitors of Ardua Hall pay respect to her statue by leaving eggs (a sign of fertility), oranges (to suggest the swell of pregnancy), croissants (to reference the moon and thus the menstrual cycle).
"Ardua" is Latin for "adversity." "Per ardua ad astra" is the official motto of the British, Australian, and New Zealand Royal Air Forces (and the Canadian Royal Air Force until 1968), meaning "through struggle to the stars." Ardua Hall's own motto is "Per Ardua Cum Estrus," approximating to "through struggle by heat (i.e. the menstrual cycle." The official translation is "Through childbirth labour with the female reproductive cycle." A common saying, given the Aunts' ability to read and write, is "Pen Is Envy." (A pun on penis envy)