Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction Moment Theory is not a new subject; however in classical treatments the ill posedness of the problem is not taken into account hence this monograph. Assuming a true solution to be uniquely determined by a sequence of moments (given as integrals) of which only finitely many are inaccurately given the authors describe and analyze several regularization methods and derive stability estimates. Mathematically the task often consists in the reconstruction of an analytic or harmonic function as is natural from concrete applications discussed (e.g. inverse heat conduction problems Cauchys problem for the Laplace equation gravimetry). The book can be used in a graduate or upper undergraduate course in Inverse Problems or as supplementary reading for a course on Applied Partial Differential Equations. Introduction Mathematical Preliminaries Regularization of moment problems by trancated expansion and by the Tikhonov method Backus Gilbert regularization of a moment problem The Hausdorff moment problem: regularization and error estimates Analytic functions: reconstruction and Sinc approximations Regularization of some inverse problems in potential theory Regularization of some inverse problems in heat conduction Epilogue References Index.