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Previous work with spatial database systems has dealt mostly with two dimensions and more with implementation than with design issues. This dissertation deals with the formal design of three- dimensional spatial database systems and with the need for abstraction in the design. Use of abstraction in the formal design of data models allows a database system developer to consider the comprehensive needs of users at an ideal level unencumbered by implementation details. The dissertation also presents a set of robust three- dimensional geometric primitives that could form the core of a discrete data model. Although a discrete data model is more concrete than SPAL3D, it has some abstraction. The dissertation offers a precise and conceptually clean specification and foundation for implementing a Database Management System (DBMS) extension for three-dimensional data. Assuming the existence of an implementation of this type system, it demonstrates the embedding of the spatial data types as attribute data types in database schemas as well as the incorporation of the operations and predicates into queries formulated in a possible extension of SQL.