Relational algebra is the set of formal operations that act on relations and produce new relations as results. Because every operation takes one or more tables as input and returns a table, the operations can be combined and chained, which lets complex queries be built up from a few simple, well-defined building blocks.
The core operations include selection, which keeps only the rows that satisfy a condition; projection, which keeps only certain columns; and the set operations union, intersection, and difference. The join combines rows from two relations that share matching values, which is how separate tables are brought together in a query. Codd introduced these operations as part of the relational model in his 1970 paper, giving database queries a precise mathematical basis.
Because relational algebra is grounded in mathematics, expressions written in it have well-defined meanings and obey algebraic laws. Two different expressions can be proven to produce the same result, which means a database system can rewrite a query into an equivalent but cheaper form. This is the foundation of query optimization, the part of a database that decides how to execute a request efficiently.
In his 1981 Turing Award lecture, Codd emphasized that this firm theoretical footing was not just elegant but practical: it let high-level, non-procedural query languages like SQL be defined, understood, and executed reliably. Relational algebra is what connects the simple table-based view that users see to the efficient machinery that runs underneath.