This monograph deals with the problems of mathematical physics which are improperly posed in the sense of Hadamard.The first part covers various approaches to the formulation of improperly posed problems. These approaches are illustrated by the example of the classical improperly posed Cauchy problem for the Laplace equation.The second part deals with a number of problems of analytic continuations of analytic and harmonic functions.The third part is concerned with the investigation of the so-called inverse problems for differential equations in which it is required to determine a dif­ ferential equation from a certain family of its solutions.