This series comprises papers that were likely kept by Thomas Hobbes and relate to his correspondence and connections with other scholars. The following were likely enclosures with letters to Hobbes: HS/E/4 letter from Christiaan Huygens to Andrew Crooke; HS/E/7 A defence of Hobbes's views on ecclesiastical authority and HS/E/6 Poem in praise of Hobbes. One item relates to his other interests: HS/E/3 is "A note of prospective glasses bought of Mr Hobbes".
Most importantly this series includes Hobbes's catalogue of the library at Hardwick (HS/E/1A) which he compiled in the late 1620s but continued to use and add to on his return to the Cavendish household in the early 1650s. It also includes notes of books and authorities written by Robert Payne and probably acquired with the other papers belonging to Payne after his death in 1651 (HS/E/1, HS/E/2 and HS/E/5). As with other material by Payne in this collection, the lists were assumed to be Hobbes's in autograph in the past.