This book presents a unifying theoretical framework for iterative solvers for linear systems. The focus is on parameter-free methods, i. e. methods that can be applied without a priori knowledge of inner properties of the systems. Despite the generality of the approach convergence estimates and geometrical properties can be derived. State-of-the-art solvers are surveyed and classified. Many new relations between these methods are furnished leading to a deeper insight. Existing gaps in the theory are pointed out and some visions for the design of more efficient and robust solvers are given. A valuation of established methods based on the theoretical results and on numerical tests is given. Recipes for the application of particular techniques are derived. The criteria are efficiency, robustness and the possibility of parallelization. This book has a triple aim: to simplify the analysis by a unified theory, to survey and valuate state-of-the-art solvers and to give an introduction to iterative solvers for non-experts in the field.