This is the fourth and revised edition of a well-received book that aims at bridging the gap between the engineering course of tensor algebra on the one side and the mathematical course of classical linear algebra on the other side. In accordance with the contemporary way of scientific publications, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this monograph addresses graduate students as well as scientists working in this field. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.

Prof. Itskov studied Automobile Engineering at the Moscow State Automobile and Road Technical University, Russia. In 1990 he received his doctoral degree in mechanics, and in 2002 he obtained his habilitation degree in mechanics from the University of Bayreuth, Germany. Since 2004 he has been full professor for continuum mechanics at the RWTH  Aachen University, Germany. His research interests comprise tensor analysis, non-linear continuum mechanics, in particular the application to anisotropic materials, as well as the mechanics of elastomers and soft tissues in a broad sense.

Vectors and Tensors in a Finite-Dimensional Space.- Vector and Tensor Analysis in Euclidean Space.- Curves and Surfaces in Three-Dimensional Euclidean Space.- Eigenvalue Problem and Spectral Decomposition of Second-Order Tensors.- Fourth-Order Tensors.- Analysis of Tensor Functions.- Analytic Tensor Functions.- Applications to Continuum Mechanics.