'Galileo's Thinking Hand' represents a fundamental revision of the earlier work 'Galileo, the Artist' published in 2007. The sections incorrectly identifying a forgery as the work of Galileo have been corrected. The work sheds light on the artistic aspects of Galileo's research life, drawing on a greatly expanded documentational basis. New insights reveal Galileo's working methods as he explored the moon, sun, moons of Jupiter, and the fixed stars