This volume presents a unified approach to the solution of ill-posed problems, based on the concept of a regularizing algorithm (RA). This idea is then explored in depth in the discussion of topics such as common conditions for the existence of regularizing algorithms, necessary and sufficient conditions of the approximations for linear problems, and the principle of iterative regularization for nonlinear problems. The majority of these issues have not previously been discussed in a monograph on ill-posed problems. The efficiency of many of the suggested algorithms will prove useful in their application to a wide range of practical problems. This volume can be read by anyone with a basic knowledge of functional analysis. This book will be of interest to applied mathematicians, engineers, and specialists in inverse problems.