The moment problem in mathematics focuses on a measure within a sequence over a temporal period. Issues associated with the moment problem involve probability theory as a measure of mean, variance, and so on. This text, written by a leading Soviet mathematician, provides a classic treatment of such topics that also involve: • Linear algebra • Probability theory • Stochastic processes • Quantum fields • Signal processing and other related subjects. The treatment, which derives from lectures delivered by the author at Kharkov University, addresses infinite Jacobi matrices and their associated polynomials, the power moment problem, function theoretic methods in the moment problem, inclusion of the power moment problem in the spectral theory of operators, and trigonmetric and continuous analogies. For mathematicians and graduate-level educators and students.