With the increasing demands of new database applications such as OLAP, data warehousing and data mining, a need arises for an extension of current database systems, which implement SQL2 [DD93] standards. These applications in fact use new and complex aggregates extensively. SQL2 supports only five built-in aggregates and provides no mechanism to define new aggregates. Approaches based on ad-hoc extensions and procedurally defined aggregates have been tried, but have proven unsatisfactory due to their rigidity and complexity. A better approach is to have extensible, user-definable aggregates. Such an approach will let the user define complex aggregates, as needed to support specific classes of new applications.