TheTheory of the Top attained its great fame from both its monum- tal scope and its outstanding authors. In the early twentieth century, Felix Klein was known as a mathematician of world fame; Arnold S- merfeld, Kleins disciple, had acquired his reputation as a rising star of theoretical physics. By 1910, when the ?nal volume of this tr- tise was published, the names of Klein and Sommerfeld would signal to a student that a matter as complex as the top was presented in a most authoritative manner, from the perspective of both mathem- ics and physics. The work also stands out in other regards: by its sheer extentfour volumes comprising a total of almost a thousand pagesand by the time lag of about ?fteen years between inception and completion. Klein himself regarded the ?nal result as somewhat disjointed. Its idiosyncratic disposition, he re?ected in 1922, may be understood only by taking into account the historic circumstances at its inception in 1895; the developments between the ?rst and last parts derailed the project from its intended course, so that for the technical applications described in Volume IV almost no use was made of the theoretical framework developed atthebeginning[Klein 1922, p. 659]. Itseemsappropriate,therefore,torecallthehistoricalcircumstances under which this treatise was conceived and pursued. Felix Klein was not only a renowned mathematician, but also an entrepreneurial and ambitious university professor striving for a broader acknowledgment of mathematics as a cultural asset.

to the Kinematics and Kinetics of the Top.- The kinematics of the top.- to kinetics (statics and impulse theory).- The Euler equations with further development of the kinetics of the top.