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This work deals with economic and flexible regular methods for solving ill-posed (unstable) problems. These methods take into account additional information on the desired solution. The authors have considered the following unstable problems: linear and nonlinear integral equations, the finite-moment problem, mathematical programming problems, spectral problems and variational inequalities. This book should be of interest to researchers in the field of mathematics and physics, as well as to those working in the field of inverse problems and applications.