  In this study, we present profiles of some distinguished graduates in
mathematics of the Jagiellonian University from the years 1918-1939. We discuss
their professional paths and scholarly achievements, instances of scientific
collaboration, connections with other academic centers in Poland and worldwide,
involvement in mathematical education and teacher training, as well as their
later roles in Polish scientific and academic life. We also try to understand
in what way they were shaped by their studies and how much of Krak\'ow
scientific traditions they continued. We find strong support for the claim that
there was a distinct, diverse and deep mathematical stream in Krak\'ow between
the wars, rooted in classical disciplines like differential equations and
geometry, but also open to new trends in mathematics. Part I concerns the
graduates before the university reform, in 1918-1926.
