In this dissertation, we present an extended relational model to represent indefinite and maybe kinds of incomplete information. A data structure, called an I-table, is defined which is capable of representing indefinite and maybe information. The information content of an I-table is precisely defined and some properties of I-tables are characterized. Redundancy in I-tables is discussed and an operator to remove it is presented. The relational algebra is then suitably extended to operate on I-tables. A correctness criterion is presented and the extended relational algebraic operations are shown to satisfy the correctness criterion. Queries are answered in the same way as with the regular relational algebra, however we may now expect indefinite and maybe answers to queries. The extended relational algebra is then used to implement a subclass of indefinite deductive databases. A special class of non-Horn rules, called I-rules, is defined. An additional operator, called project-union, which is a further extension to the extended projection operator is presented. The project-union operator is used to evaluate I-rules. The correctness of the algebraic approach to indefinite e deductive databases is established. Finally, we present generalized I-tables, called M-tables, which are capable of representing more general forms of indefinite information. The relational algebra is further generalized to operate on M-tables. Additional operators, R-projection and merge, are defined to answer queries about M-tables.