Materialized XML views are a popular technique for integrating data from possibly distributed and heterogeneous data sources. However, the problem of the incremental maintenance of such XML views poses new challenges which to date remain unaddressed. One, XML views not only filter the data, but may radically restructure it to construct new XML nested document structures. Moreover, order is inherent in the XML model, and XML views reflect both the implicit document order of the underlying sources and the order explicitly imposed in the view definition. Therefore, order also has to be preserved at view maintenance time. In this thesis we present an algebraic approach for the incremental maintenance of XQuery views, called VOX (View maintenance for Ordered XML). To the best of our knowledge, this is the first solution to order-preserving XML view maintenance. Our strategy correctly transforms an update to source XML data into sequences of updates that refresh the view. Our technique is based on an algebraic representation of the XQuery view expression using an XML algebra. The XML algebra has ordered bag semantics; hence most of the operators logically are order preserving. We propose an order-encoding mechanism that migrates the XML algebra to (non-ordered) bag semantics, no longer requiring most of the operators to be order-aware. Furthermore, this now allows most of the algebra operators to become distributive over update operations. This transformation brings the problem of maintaining XML views one step closer to the problem of maintaining views in other (unordered) data models. We are thus now able to adopt some of the existing (relational) maintenance techniques towards our goal of efficient order-sensitive XQuery view maintenance. In addition we develop a full set of rules for propagating updates through XML specific operations. We have proven the correctness of the VOX view maintenance approach. A full implementation of VOX on top of RAINBOW, the XML data management system developed at WPI, has been completed. Our experimental results performed using the data and queries provided by the XMark benchmark, confirm that incremental XML view maintenance indeed is significantly faster than complete recomputation in most cases. Incremental maintenance is shown to outperform recomputation even for large updates.