Matrices with structure are encountered in a wide variety of problems in pure and applied mathematics, and in engineering. Matrix patterns and structural properties provide a uniform means for describing apparently different features of the problems that they model. This book collects a set of contributions in structured matrix computations that covers different facets of the problems involved in this research area. The book may be naturally divided into four parts: the first part contains two contributions on asymptotical spectral properties of structured matrices. The second part contains seven contributions related to algorithm design and analysts. The third part, consisting of three contributions, concerns issues specifically related to structures, algebras and polynomials. The fourth part concerns applications to image processing and differential equations.