Inverse Scattering with Rational Scattering Coefficients and Wave Propagation in Nonhomogeneous Media -- Aluthge Transforms and the Convex Hull of the Spectrum of a Hilbert Space Operator -- Maximal Nevanlinna-Pick Interpolation for Points in the Open Unit Disc -- On the Numerical Solution of a Nonlinear Integral Equation of Prandtl’s Type -- Fourier Integral Operators and Gelfand-Shilov Spaces -- Strongly Regular J-inner Matrix-valued Functions and Inverse Problems for Canonical Systems -- Regularization Processes for Real Functions and Ill-posed Toeplitz Problems -- Minimal State-space Realization for a Class of nD Systems -- Continuity in Weighted Besov Spaces for Pseudodifferential Operators with Non-regular Symbols -- A New Proof of an Ellis-Gohberg Theorem on Orthogonal Matrix Functions Related to the Nehari Problem -- Schur-type Algorithms for the Solution of Hermitian Toeplitz Systems via Factorization -- Almost Pontryagin Spaces -- Multivariable ?-contractions -- The Singularly Continuous Spectrum and Non-Closed Invariant Subspaces -- Numerical Methods for Cauchy Singular Integral Equations in Spaces of Weighted Continuous Functions -- On a Gevrey-Nonsolvable Partial Differential Operator -- Optimal Prediction of Generalized Stationary Processes -- Symmetries of 2D Discrete-Time Linear Systems -- An Algorithm for Solving Toeplitz Systems by Embedding in Infinite Systems -- Fredholm Theory and Numerical Linear Algebra -- Additive and Multiplicative Perturbations of Exponentially Dichotomous Operators on General Banach Spaces -- Factorization of Block Triangular Matrix Functions with Off-diagonal Binomials -- Closely Connected Unitary Realizations of the Solutions to the Basic Interpolation Problem for Generalized Schur Functions -- Trace-Class Weyl Transforms.Thisvolumecontainsaselectionofpapersinmodernoperatortheoryanditsapp- cations. Most of them are directly related to lectures presented at the Fourteenth International Workshop on Operator Theory and its Applications (IWOTA 2003) held at the University of Cagliari, Italy, in the period of June 24–27, 2003. The workshop, which was attended by 108 mathematicians – including a number of PhD and postdoctoral students – from 22 countries, presented eight special sessions on 1) control theory, 2) interpolation theory, 3) inverse scattering, 4) numerical estimates for operators, 5) numerical treatment of integral equations, 6) pseudodi?erential operators, 7) realizations and transformations of analytic functions and inde?nite inner product spaces, and 8) structured matrices. The program consisted of 19 plenary lectures of 45 minutes and 78 lectures of 30 minutes in four parallel sessions. The present volume re?ects the wide range and rich variety of topics p- sentedanddiscussedattheworkshop,bothwithinandoutsidethespecialsessions. The papers deal with inverse scattering, numerical ranges, pseudodi?erential - erators, numerical analysis, interpolation theory, multidimensional system theory, inde?nite inner products, spectral factorization, and stationary processes. SinceintheperiodthattheproceedingsofIWOTA2003werebeingprepared, Israel Gohberg, the president of the IWOTA steering committee, reached the age of 75, we decided to dedicate these proceedings to Israel Gohberg on the occasion of his 75th birthday. All of the authors of these proceedingshavejoined the editors and dedicated their papers to him as well.