In the same year that Galileo published The Assayer, Grassi delivered these lectures to Jesuit students in the Rome College (Collegio Romano). Grassi describes Galileo’s discovery of mountains on the Moon, discusses the satellites of Jupiter, and interprets sunspots as imperfections on the surface of the Sun. This manuscript, never published and new to scholars, was acquired in 2012 through the generous support of the OU Athletic Department.