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In this paper, we present a temporal, object-oriented algebra which serves as a formal basis for the query language of a temporal, object-oriented data model. Our algebra is a superset of the relational algebra in that it provides support for manipulating temporal objects, temporal types, type hierarchies and class lattices, multiple time-lines, and correction sequences in addition to supporting the five relational algebra operators. Graphs are used as the visual representations of both the schema and the object instances. The algebra provides constructs to modify and manipulate the schema graph and its extension, the object graph. The algebra operates on a collection or collections of objects and returns a collection of objects. This algebra is a first step in providing a formal foundation for query processing and optimizing in a temporal, object-oriented data model.