  In the second half of the 1920s, physicists and mathematicians introduced
group theoretic methods into the recently invented ``new'' quantum mechanics.
Group representations turned out to be a highly useful tool in spectroscopy and
in giving quantum mechanical explanations of chemical bonds. H. Weyl explored
the possibilities of a group theoretic approach towards quantization. In his
second version of a gauge theory for electromagnetism, he even started to build
a bridge between quantum theoretic symmetries and differential geometry. Until
the early 1930s, an active group of young quantum physicists and mathematicians
contributed to this new challenging field. But around the turn to the 1930s,
opposition against the new methods in physics grew. This article focusses on
the work of those physicists and mathematicians who introduced group theoretic
methods into quantum physics.
