  This is mainly a translation of Proc. of the 29th Symp. on History of
Mathematics, Tsuda University, held Oct. 2018, of my talk. The first occasion
when I studied the history of the theory of invariant integrals (or measures)
was an unintended opportunity where I was asked to write "Kaisetsu"
(explanatory and commentary article) to the new book of Prof. M. Saito, a first
translation into Japanese of the famous Weil's book "L'int\'egrations dans les
groupes topologiques et...". Personally, for my professional work, it was
needed only to read this Weil's original book and several text books on measure
theory. For writing the Kaisetsu mentioned above, other than several
mathematical papers and also Weil's non-mathematical works, it was sufficient
for me to read Haar's original paper roughly and similarly for other historical
classics. Thus I felt the necessity of further study and now I make intendedly
a historical study. Reading original papers due to Hurwitz, Schur, Weyl and so
on in detail, I explain their contents from my point of view, and give the
relationships among them. I make intendedly a historical study. Reading
original papers due to Hurwitz, Schur, Weyl and so on in detail, I explain
their contents from my point of view, and give the relationships among them.
