A field of mathematics that deals with groupings of data. It is one of the foundations of relational theory.

Set theory is the mathematical theory of sets, which represent collections of abstract objects. It encompasses the everyday notions, introduced in primary school, of collections of objects, and the elements of, and membership in, such collections. In most modern mathematical formalisms, set theory provides the language in which mathematical objects are described.

In music, musical set theory provides concepts for categorizing musical objects and describing their relationships. Many of the notions were first elaborated by Howard Hanson in connection with tonal music, and then mostly developed in connection with atonal music; the concepts of set theory are very general and can be applied to tonal and atonal styles in any equally-tempered tuning system, and to some extent more generally than that. Musical set theory deals with collections of pitches and pitch classes, which may be ordered or unordered, and which can be related by musical operations such as transposition, inversion, and complementation.