This dissertation presents an initial study of the concepts and algorithms for generic model management. We describe the first prototype of a generic model management system, introduce the algebraic operators that are used to manipulate models and mappings, clarify the semantics of the operators, and develop novel algorithms for implementing them. In particular, we present an innovative algorithm based on fixpoint computation that is used for implementing the generic operator Match, which finds correspondences between two models. Using the prototype and the operators presented in the dissertation, we develop solutions for several practically relevant problems, such as change propagation and reintegration.