Many problems in various applications of mathematics in physics and engineering lead to a search for a solution of large linear systems with Toeplitz or Toeplitz-related matrices. In recent years, a lot of research has focused on such systems. The book deals primarily with iterative methods, pre-conditioners and applications. It is divided into three parts. The first part (Introduction) deals with basic concepts and results in linear algebra (especially the conjugate gradients method). No specific applications are mentioned here. The second part (Theory) contains a discussion of solutions of Toeplitz systems. This includes direct, and in particular iterative, methods with theoretical background for using circulant and non-circulant matrices as pre-conditioners. The author also discusses ill-conditioned Toeplitz systems or Toeplitz-like systems. The third part (Applications) provides a theoretical framework for various fields of use. Here partial differential equations, queuing networks, signal and image processing and integral equations are considered. The book gives an excellent overview of the research and results in this area during the last few decades. The book may attract interest from graduate students, mathematicians and other specialists working in applied mathematics and scientific computing.