The purpose of this volume is to give an up-to-date introduction to tensor valuations and their
applications. Starting with classical results concerning scalar-valued valuations on the
families of convex bodies and convex polytopes it proceeds to the modern theory of tensor
valuations. Product and Fourier-type transforms are introduced and various integral formulae
are derived. New and well-known results are presented together with generalizations in several
directions including extensions to the non-Euclidean setting and to non-convex sets. A variety
of applications of tensor valuations to models in stochastic geometry to local stereology and
to imaging are also discussed.
