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This book is the third edition of the 1999 lecture notes of the courses on interpolation theory that the author delivered at the Scuola Normale in 1998 and 1999. In the mathematical literature there are many good books on the subject, but none of them is very elementary, and in many cases the basic principles are hidden below great generality. In this book the principles of interpolation theory are illustrated aiming at simplification rather than at generality. The abstract theory is reduced as far as possible, and many examples and applications are given, especially to operator theory and to regularity in partial differential equations. Moreover the treatment is self-contained, the only prerequisite being the knowledge of basic functional analysis.

Mathematics. --- Functional analysis. --- Operator theory. --- Numerical analysis. --- Functional Analysis. --- Numerical Analysis. --- Operator Theory. --- Mathematical analysis --- Functional analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Interpolation spaces.