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;...