Schikore, Daniel R. Ph.D., Purdue University, August 1997. Interactive Visualization of Multidimensional Scientific Data. Major Professor: Chandrajit L. Bajaj. Scientific data visualization concerns the manipulation of sampled and computed data for comprehensive display_ The goal of the visualization is to bring to the user a deeper understanding of the data, as well as any underlying physical laws and properties. In this thesis, we review the techniques contributing to interactive visualization of multidimensional and multivariate data. We describe a set of tools which we have developed for interactive data visualization, exploration, and interrogation. Our work draws on the fundamentals of data field representations and properties as well as efficient hierarchical structures for processing and querying data. We describe a novel approach for simplifying meshes with guaranteed error bounds in both geometry and associated functions, and demonstrate the ability to build multiresolution hierarchical representations using our approach. vVe introduce a new computational framework for the extraction of isocontours from scalar valued data. The search for cells intersected by an isocontour is accelerated through the use of range query data structures. We present three seed set construction algorithms, of varying complexity and performance, which reduce the storage requirements of the search structure without penalty in the query complexity. We analyze three search structures of varying space and query complexity, demonstrating that our approach of reducing the size of the search structure introduces additional freedom in the overall algorithm architecture, allowing adaptation to application dependent problems. We conclude with a discussion of open problems and extensions.