  During the ``long decade'' of transformation of mathematical physics between
1915 and 1930, H. Weyl interacted with physics in two highly productive phases
and contributed to it, among others, by his widely read book on {\em Space -
Time - Matter (Raum Zeit - Materie)} (1918 -- 1923) and on {\em Group Theory
and Quantum Mechanics (Gruppentheorie und Quantenmechanik)} (1928 - 1931). In
this time Weyl's understanding of the constitution of matter and its
mathematical description changed considerably. At the beginning of the period
he started from a "dynamistic" and geometrical conception of matter, following
and extending the Mie-Hilbert approch, which he gave up during the year 1920.
After transitional experiments with a singularity (and in this sense
topological) approach in 1921/22, he developed an open perspective of what he
called an ``agency theory'' of matter. The idea for it was formulated already
before the advent of the ``new'' quantum mechanics in 1925/26. It turned out to
be well suited to be taken over to the quantum view as a kind of ``heritage''
from the first half of the decade. At the end of the period, Weyl completely
renounced his earlier belief in the possibility to ``construct matter'' from a
geometrically unified field theory. He now posed the possibility of a
geometrization of the mathematical forms underlying the rising quantum physical
description of matter as a completely open problem for future research.
