"The material, forming a perfect integral whole, offers information that puts the reader at the forefront of current research and determines fruitful directions for future advanced study. Clarity of the text and rigorous proofs represent other features of this monograph. The monograph is addressed to researchers and graduate students specializing in pure and applied mathematics who are interested in a modern approach to discrete approximation theory." Mathematical Reviews Clippings In this monograph, we present the authors' recent work of the last seven years in Approximation Theory. Chapters are self-contained and can be read independently and advanced courses can be taught out of this book. Here our generalized discrete singular operators are of the following types: Picard, Gauss-Weierstrass and Poisson-Cauchy operators. We treat both the unitary and non-unitary, univariate and multivariate cases of these operators, which are not necessarily positive operators. The book's results are expected to find applications in many areas of pure and applied mathematics, and statistics. As such, it is suitable for researchers, graduate students, and seminars of related subjects, and serves well as an invaluable resource for all science libraries.