The Library has collections of renaissance and medieval manuscripts and Islamic manuscripts in both the Manuscripts and Archives Division and the Spencer Collection.
The Manuscripts and Archives Division's renaissance and medieval manuscripts, circa 850-circa 1600, are briefly described here: http://archives.nypl.
For more thorough descriptions of the Library's renaissance and medieval manuscripts, consult the following:
The primary reference for the Library's Islamic manuscripts is Barbara Schmitz's Islamic Manuscripts in the New York Public Library.