  This essay discusses the development of key geometric ideas in the 19th
century which led to the formulation of the concept of an abstract manifold
(which was not necessarily tied to an ambient Euclidean space) by Hermann Weyl
in 1913. This notion of manifold and the geometric ideas which could be
formulated and utilized in such a setting (measuring a distance between points,
curvature and other geometric concepts) was an essential ingredient in
Einstein's gravitational theory of space-time from 1916 and has played
important roles in numerous other theories of nature ever since.
