[2] He attended secondary school at Hagen and then moved on to undertake his university studies between 1908 and 1913 at Munich, Freiburg i.B., Berlin, Münster and Göttingen.
It was from the University of Münster that he received his doctorate in 1913/14 for a dissertation submitted the previous year entitled "The teachings of Hermes Trismegistus".
He stressed the extent to which the theosophical doctrines of the "thrice-greatest Hermes" were based not simply on ancient oriental teachings, as had been assumed hitherto on account of research published by Richard Reitzenstein, but also leaned heavily on Greek philosophy.
He subsequently expanded the dissertation to produce a more extensive publication which was picked out for commendation by the Vienna Academy because of the explanations it provided for inherently inscrutable traditions.
[1] In 1918, still aged only 29, he accepted an invitation to take a full professorship in Classical Philology at the Braunsberg Catholic Academy near Königsberg, then one of the largest Jesuit schools in Europe.
In January 1933 régime change at a national level quickly impacted the universities sector as the new Hitler government lost no time in transforming Germany into a one-party dictatorship: measures included steps to ensure that party members and/or supporters were installed in positions of power and influence.
The formal role of Cologne university rector was transferred to Kroll on an "acting" basis till 5 November 1945 when he was himself re-elected to the position on his own account.
In those critical post-war years he also articulated the real-world conflict between humanistic idealised calls for new beginnings in sciences and in teaching, and the pragmatic necessity sometimes to work with former National Socialist Party members.
[1] He was a founder member of the "Arbeitsgemeinschaft für Forschung des Landes Nordrhein-Westfalen" (loosely, "Extended Working Group for Research in [the newly created state of] North Rhine-Westphalia", and accepted a quasi-political appointment as Cologne "councillor" ("Beigeordneter" ) for Arts and Schooling.