Marek Golasiński is a Professor at the Faculty of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn (Poland) since 2012. He was previously Associate Professor at the Faculty of Mathematics and Computer Science, Nicolaus Copernicus University in Toruń (Poland) from 1971-2011. He was awarded the degrees of Ph.D. (1978) and Habilitation (2004), both in Algebraic Topology from the Faculty of Mathematics and Computer Science, Nicolaus Copernicus University in Toruń (Poland). He has written a previous book (with Juno Mukai) on Gottlieb and Whitehead Center Groups of Spheres, Projective and Moore Spaces.Francisco Gómez Ruiz studied mathematics at the University of Barcelona. In 1978 received his doctorate at the University of Toronto (Stephen Halperin was his advisor). After 2 years at the department of mathematics of the Autonomous University of Barcelona and one year at the University of Cantabria, he has been 33 years professor at the department of algebra, geometry and topology of the University of Malaga. He has published over 30 research articles and 3 books.

“A striking feature of the book is that elementary matrix calculus is sufficient to understand all the concepts and to carry out all the proofs, even the more involved ones, which makes it readily accessible to a wide audience … . This text remains a valuable source book for all those who seek a matrix approach to Stiefel/Grassmannian manifolds and/or need to generalize these manifolds to an arbitrary formally real Pythagorean field K.” (Giovanni Moreno, Mathematical Reviews, June, 2025)

• - 1. Algebraic Preliminaries. - 2. Exceptional Groups .G2(K) and .F4(K). - 3. Stiefel, Grassmann Manifolds and Generalizations. - 4. More Classical Matrix Varieties. - 5. Algebraic Generalizations of Matrix Varieties. - 6. Curvature, Geodesics and Distance on Matrix Varieties.