Full Idea
Set theory is that branch whose task is to investigate mathematically the fundamental notions 'number', 'order', and 'function', taking them in their pristine, simple form, and to develop thereby the logical foundations of all of arithmetic and analysis.
Gist of Idea
Set theory investigates number, order and function, showing logical foundations for mathematics
Source
Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908], Intro)
Book Reference
'From Frege to Gödel 1879-1931', ed/tr. Heijenoort,Jean van [Harvard 1967], p.200
A Reaction
At this point Zermelo seems to be a logicist. Right from the start set theory was meant to be foundational to mathematics, and not just a study of the logic of collections.