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This monograph is a study of aspect of methods solving ill-posed problems, inverse problems: the regularization methods for solving ill-posed problems with unbounded operators, variationnal inequalities, and stable approximate values of unbounded operators. The author has used extensily his earlier published papers, as well as the papers/books of other authors that were used or mentioned. Chapter 1presents Hilbert space background; Chapter 2 presents some problems leading to unbounded operators; Chapter 3 presents regularization methods solving ill-posed problems with unbounded operators; Chapter 4 presents stable methods for computing value of the unbounded linear operators; Chapter 5 presents regularization methods solving the variational inequalities with perturbation on monotone.