This volume is devoted to the use of the method of operator identities for investigating interpolation and expansion problems. A general interpolation problem comprising both classical and new elements is formulated. The solution of an abstract form of the Potapov inequality enables the description of the set of solutions of the general interpolation problem. Connections between the solved interpolation problem and important problems of analysis occurring in, for example, spectral theory, nonlinear integrable equations, and generalized stationary processes, are then considered. This book should be of interest to graduate students and researchers whose work involves approximations and expansions; operator theory; measure and integration; general mathematics systems; and Fourier analysis.