A multidimensional access method offering significant performance increases by intelligently partitioning the query space is applied to relational database management systems (RDBMS). We introduce a formal model for multidimensional partitioned relations and discuss several typical query patterns. The model identifies the significance of multidimensional range queries and sort operations. The discussion of current access methods gives rise to the need for a multidimensional partitioning of relations. A detailed analysis of space partitioning focussing especially on Z-ordering illustrates the principle benefits of multidimensional indexes. After describing the UB-Tree and its standard algorithms for insertion, deletion, point queries, and range queries, we introduce the spiral algorithm for nearest neighbor queries with UB-Trees and the Tetris algorithm for efficient access to a table in arbitrary sort order. We then describe the complexity of the involved algorithms and give solutions to selected algorithmic problems for a prototype implementation of UB-Trees on top of several RDBMSs. A cost model for sort operations with and without range restrictions is used both for analyzing our algorithms and for comparing UB-Trees with state-of-the-art query processing. Performance comparisons with traditional access methods practically confirm the theoretically expected superiority of UB-Trees and our algorithms over traditional access methods: Query processing in RDBMS is accelerated by several orders of magnitude, while the resource requirements in main memory space and disk space are substantially reduced. Benchmarks on some queries of theTPC-D benchmark as well as the data warehousing scenario of a fruit juice company illustrate the potential impact of our work on relational algebra, SQL, and commercial applications. The results of this thesis were developed by the author managing the MISTRAL project, a joint research and development project with SAP AG (Germany), Teijin Systems Technology Ltd. (Japan), NEC (Japan), Hitachi (Japan), Gesellschaft für Konsumforschung (Germany), and TransAction Software GmbH (Germany).