Abstract: This chapter presents itineraries in the history of mathematical logic from the period 1900–1935. By focusing on a narrower range of topics, the chapter improves on the existing literature on the history of logic. The itineraries include: metatheoretical properties of axiomatic systems; Bertrand Russell's mathematical logic; Zermelo's axiomatization of set theory and related foundational issues; the theory of relatives and Löwenheim's Theorem; logic in the Hilbert school; proof theory and arithmetic; intuitionism and many-valued logics; and semantics and model-theoretic notions.

Keywords: intuitionism, logic, Bertrand Russell, Zermelo, Löwenheim, Hilbert, proof theory, axiomatic systems,