The book covers fundamentals of the theory of optimal methods for solving ill-posed problems, as well as ways to obtain accurate and accurate-by-order error estimates for these methods. The methods described in the current book are used to solve a number of inverse problems in mathematical physics. ContentsModulus of continuity of the inverse operator and methods for solving ill-posed problemsLavrent’ev methods for constructing approximate solutions of linear operator equations of the first kindTikhonov regularization methodProjection-regularization methodInverse heat exchange problems