This advanced visualization course is concerned with techniques for the representation, approximation and visualization of scientific data. These topics are relevant for applications in scientific and engineering fields as well as medical and bio-medical disciplines. This course discusses several methods for the reconstruction of continuous representation, based on concepts from approximation theory (e.g., scattered data approximation, polynomial approximation, least squares approximation, hierarchical/multi-resolution approximation), with the aim at using the resulting continuous field reconstructions for effective data analysis and visualization. The course covers these methods in the context of scalar, vector and tensor field data visualization problems arising in diverse applications, including vector/flow field analysis, medical image data understanding and strain/stress data visualization.