This course provides an introduction to the metatheory of elementary logic. Following a "refresher" on the basics of notation and the use of classical logic as a representation language, we concentrate on the twin notions of models and proof. An axiomatic system of first order logic is introduced and proved complete for the standard semantics, and then we give an overview of the basic concepts of proof theory and of formal set theory. The material in this course is presupposed by other courses in the Summer School, which is why it is presented first.