When using the Laplace integral transformation to solve problems of mathematics, the problem of numerical inversion of the Laplace transformation becomes important. The proposed book explores the relationship of Laguerre series with a wide class of integral transformations of great theoretical and applied importance. Some of the expansions obtained in the book are of interest to the theory of special functions. The issues of constructing numerical algorithms and techniques for restoring the original on the basis of harmonic analysis methods have been investigated, which make it possible to increase the accuracy of determining the camp spectrum and control the accuracy characteristics of the conversion process. Some estimates of the convergence of numerical algorithms were obtained and the issues of stable summation of Laguerre series were considered. The issues of application of the camp spectrum for solving specific practical problems were investigated. An overview of the current state of the numerical inversion problem of the Laplace transform is given. The book is intended for scientific and engineering workers who, in their activities, have to deal with the theory or application of the Laplace transformation.