It is true that there exist many books dedicated to linear algebra and some- what fewer to multilinear algebra, written in several languages, and perhaps one can think that no more books are needed. However, it is also true that in algebra many new results are continuously appearing, different points of view can be used to see the mathematical objects and their associated structures, and different orientations can be selected to present the material, and all of them deserve publication. Under the leadership of Juan Ramon Ruiz-Tolosa, Professor of multilin- ear algebra, and the collaboration...