After the book "Basic Operator Theory" by Gohberg-Goldberg was pub lished, we, that is the present authors, intended to continue with another book which would show the readers the large variety of classes of operators and the important role they play in applications. The book was planned to be of modest size, but due to the profusion of results in this area of analysis, the number of topics grew larger than ex pected. Consequently, we decided to divide the material into two volumes - the first volume being presented now. During the past years, courses and seminars were given at our respective in stitutions based on parts of the texts. These were well received by the audience and enabled us to make appropriate choices for the topics and presentation for the two vol umes. We would like to thank G.J. Groenewald, A.B. Kuijper and A.C.M. Ran of the Vrije Universiteit at Amsterdam, who provided us with lists of remarks and corrections. We are now aware that the Basic Operator Theory book should be revised so that it may suitably fit in with our present volumes. This revision is planned to be the last step of an induction and not the first. I. Riesz projections and functional calculus.- II. Eigenvalues of finite type.- III. Analytic equivalence.- IV. Linear operator pencils.- V. Spectral theory for bounded selfadjoint operators.- VI. Singular values of compact operators.- VII. Trace and determinant.- VIII. Hilbert-Schmidt operators.- IX. Integral operators with semi-separable kernels.- X. The growth of the resolvent operator and applications to completeness.- XI. Fredholm operators.- XII. Wiener-Hopf integral operators.- XIII. Wiener-Hopf integral operators with rational symbols.- XIV. Unbounded linear operators.- XV. Functional calculus for unbounded operators.- XVI. Unbounded selfadjoint operators.- XVII. Unbounded Fredholm operators and perturbation theorems.- XVIII. A class of ordinary differential operators on a half line.- XIX. Strongly continuous semigroups.- Standard references texts.- List of symbols.
