This volume contains English translations of 13 groundbreaking papers on Toeplitz matrices and Wiener-Hopf equations and other classes of discrete and continuous convolution operators and singular integral equations. The papers are both of theoretical and numerical interest. In particular, the papers examine fast algorithms for inversion of these operators, the theory of discrete and continuous resultants, inversion via factorization, and symbol construction. Originally the papers were written in Russian more than thirty years ago; their English translation is published here for the first time. These papers solved difficult problems and opened new venues in the above-mentioned areas. They are still frequently quoted, and moreover, they exert a continuing influence on numerical analysis and other areas of Pure and Applied Mathematics and Engineering. The book is addressed to a wide audience of mathematicians and engineers, from graduate students to researchers, whose interests lie in the above-mentioned areas.