Iterative methods are an important and fundamental class of solution algorithms that are used by scientists and engineers. Their applications can be found in diverse fields of science, engineering and technology, for example, computational fluid dynamics, queuing and communication problems, and image and signal processing. Because of the rapid evolution of the development of this field, as well as the fact that iterative methods are not often developed in a generic form for general applications, there is a lack of published materials that treat the topic properly and fully. These lectures from the Winter School on Iterative Methods in Scientific Computing and their Applications aims to bridge such a gap in the literature. This book provides an excellent overview of the state-of-the-art of the field as well as being a general intoduction for beginners. It will prove useful to researchers, practitioners and engineers interested in practising scientific computing.