The author is working in the field of numerical mathematics for partial differential equations and integral equations. He has published monographs, e.g., about the multi-grid method, about the numerical analysis of elliptic pdes, about iterative solution of large systems of equation, and about the technique of hierarchical matrices.

• Part I: Algebraic Tensors.- Introduction.- Matrix Tools.- Algebraic Foundations of Tensor Spaces.- Part II: Functional Analysis of Tensor Spaces.- Banach Tensor Spaces.- General Techniques.- Minimal Subspaces.-Part III: Numerical Treatment.- r-Term Representation.- Tensor Subspace Represenation.- r-Term Approximation.- Tensor Subspace Approximation.-Hierarchical Tensor Representation.- Matrix Product Systems.- Tensor Operations.- Tensorisation.- Generalised Cross Approximation.- Applications to Elliptic Partial Differential Equations.- Miscellaneous Topics.- References.- Index.

"The present book Tensor spaces and numerical tensor calculus by Wolfgang Hackbusch to a large extent fills the gap between theory on finite-dimensional tensor spaces and tensor computations. It also gives a comprehensive overview of numerical tensor computations. ... the book is most useful as a (very rich) source book for researchers in the area. It might also be used as a textbook for a Ph.D. course ... ." (Lars Elden, Mathematical Reviews, October, 2015)