Relational algebra is the formal description of how a relational database operates and the underlying mathematics of SQL operations. There are two groups of relational algebra operators: set operations like union, intersection, and difference; and special database operations like select, project, and join. The project operation selects a subset of attributes from a relation, while select retrieves tuples that satisfy a given condition. These operations can be combined, such as to select employee numbers for employees in a particular department.