1. Interpolation problems play an important role both in theoretical
and applied investigations. This explains the great number of works
dedicated to classical and new interpolation problems ([1)-[5], [8),
[13)-[16], [26)-[30], [57]). In this book we use a method of
operator identities for investigating interpo- lation problems.
Following the method of operator identities we formulate a general
interpolation problem containing the classical interpolation problems
(Nevanlinna- Pick, Caratheodory, Schur, Humburger, Krein) as particular
cases. We write down the abstract form of the Potapov inequality. By
solving this inequality we give the description of the set of solutions
of the general interpolation problem in the terms of the
linear-fractional transformation. Then we apply the obtained general
results to a number of classical and new interpolation problems. Some
chapters of the book are dedicated to the application of the interpola-
tion theory results to several other problems (the extension problem,
generalized stationary processes, spectral theory, nonlinear integrable
equations, functions with operator arguments). 2. Now we shall proceed
to a more detailed description of the book contents.