The use of the preconditioned conjugate gradient method with circulant preconditioners to solve Toeplitz systems was proposed in 1986. In this short book，the author mainly studies some well-known preconditioners from a theoretical viewpoint. An application of preconditioners to systems of ordinary differential equations is also discussed. The book contains several important research results on iterative Toeplitz solvers obtained in recent years. It could be accessible to senior undergraduate students who， in various scientific computing disciplines， have a basic linear algebra， calculus， numerical analysis， and computing knowledge.The book is also useful to researchers and computational practitioners who are interested in fast iterative Toeplitz solvers.

　　Dr. Xiao-Qing Jin is a Professor at the Department of Mathematics， University of Macau. He is the author of 4 books and over 70 research papers. He is also a member of the editorial beards of Journal on Numerical Methods and Computer Applications， Numerical Mathematics： Theory， Methods and Applications， and East Asia Journal of Applied Mathematics.