This book applies functional analysis and complex analysis to problems of interpolation in spaces of analytic functions. It examines problems of recovery--producing approximations to functions from measured values. These values may in turn be corrupted by small errors; the book discusses methods for producing good models using this partial and inaccurate information. The practical applications include systems identification, signal processing, and sampling. The book provides mathematical introductions to many important areas of current research, including H( control theory, sampling and systems processing, and the theory of worst-case identification. This is the first formal treatment of worst-case identification, a field where the author is a leading authority, and the discussion includes much practical material on input design and identification algorithms. This material is appropriate for a graduate-level course on function spaces and the operators acting on them.