The book "Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data" offers a comprehensive and illustrative presentation of current research in an emerging field of mathematics and natural sciences. Originating from the fourth Dagstuhl conference on this topic in 2011, it addresses a variety of subjects ranging from the analysis of tensor fields to their mathematical and analytical properties. The first section is dedicated to the visualization of tensors and tensor fields in engineering, while the second section focuses on the representation and processing of higher order descriptors. Innovative mathematical techniques are introduced that are significant for the processing of vector images and the analysis of diffusion data. The third section provides an in-depth mathematical analysis that enables the modeling of complex diffusion data such as high-angular resolution diffusion imaging (HARDI). The book is aimed at professionals and students who wish to engage with the latest developments in tensor processing and visualization.