A set is a well-defined collection of distinct objects, considered as a single mathematical object.
Sets are denoted by curly braces: A = {1, 2, 3}. Key operations include union (AāŖB), intersection (Aā©B), complement (A'), difference (A-B), and Cartesian product (AĆB). Sets can be finite or infinite. Set theory provides the foundation for all modern mathematics. Subsets, power sets, and Venn diagrams are key concepts.
Set theory was founded by Georg Cantor in the late 19th century. His work on infinite sets was initially controversial but became fundamental. Bertrand Russell discovered Russell's Paradox in 1901, leading to axiomatic set theories by Zermelo and Fraenkel (ZF set theory). Set theory is now considered the foundation of mathematics.