1.Mathematical preliminaries. 2.Regularizations of momento problems by truncated expansión and by the Tiknonov method. 3.Backus-Gilbert regulatization of a moment problem. 4.The Hausdorff moment: regularization and error estimaes. 5.Anality functions reconstruction ans sinc approximations. 6.Regularization of some inverse problems in potential theory. 7.Regularization of some inverse problems in heat conduction. 8.Epilogue.