Since antiquity mathematicians have spoken of classes, multitudes, and sets, but set theory as such is a product of the 19th century (Bernard Bolzano, Georg Cantor, Richard Dedekind, et al.). Not until the 20th century did set theory attain an axiomatic foundation (Ernst Zermelo, Thoralf Skolem, Johann von Neumann, Paul Bernays, Wilhelm Ackermann, et al.). In this essay we discuss Zermelo's paper "Investigations in the foundations of set theory I" (Investigations for short). In order fully to appreciate Zermelo's research we must discuss the 19th century emergence of the concept of set as a terminus technicus of mathematics as well as the axiomatic method with all its many facets.