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This Element will offer a concise introduction to set theory, a branch of mathematics with a special subject matter, the infinite, but also a general framework for all modern mathematics, whose notions figure in every branch, pure and applied.

One is often said to be reasoning well when they are reasoning logically. Many attempts to say what logical reasoning is have been proposed, but one commonly proposed system is first-order classical logic. This Element will examine the basics of first-order classical logic and discuss some surrounding philosophical issues.

An exposition of second- and higher-order logic and type theory. It includes the syntax and semantics of classical second-order logic and a discussion of higher-order logic based on the concept of a type. Also explored are origins and nature of type theory, its relationship to set theory, and descriptions of contemporary forms of type theory.