Heinz Hopf was a mathematician who recognized important mathema-
tical ideas and new mathematical phenomena through special cases. In the
simplest background the central idea or the difficulty of a problem
usually becomes crystal-clear. Doing geometry in this fashion is a
joy. Hopf's great insight allows this approach to lead to serious ma-
thematics, for most of the topics in these notes have become the star-
ting-points of important further developments. I will try to mention a
few. excerpt from the preface by S.S Chern of
Differential Geometry in the Large by H.Hopf
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