this volume presents new results in regularization of ill-posed problems by iteration methods, which is one of the most important and rapidly developing topics of the theory of ill-posed problems. the new theoretical results are connected with the proposed united approach to the proof of regularizing properties of the `classical iteration methods (steepest descent, conjugate direction) complemented by the stopping rule depending on the level of errors in the input data. much emphasis is given to the choice of the iteration index as the regularization parameter and to the rate convergence estimates of the approximate solutions. results of calculations for important applications in non-linear thermophysics are also presented. audience: this work will be a useful resource for specialists in the theory of partial differential and integral equations, in numerical analysis and in theory and methods.