Partially ordered sets. Equivalence relations. Well-ordered sets. Elementary axioms of set theory: The axiom of extensionality, pairing axiom, the axiom of infinity, power set axiom, xiom of replacement. Transitive sets. Regularity. ordinal numbers. Axiom of choice. Four forms of axiom of choice. Foundation of mathematics. Cardinality. Ordinal arithmetic. Cardinal arithmetic. Cofinality.