Spectral Theory of Operators on Hilbert Spaces Preface Preliminaries Spectrum Spectral Theorem Functional Calculus Fredholm Theory References Index. This work is intended to provide a concise introduction to the spectral theory of Hilbert space operators. With an emphasis on detailed proofs and recent aspects of theory it can serve as a modern textbook for a first graduate course in the subject. The coverage of topics is thorough exploring various intricate points and hidden features often left untreated. The book begins with a primer on Hilbert space theory summarizing the basics required for the remainder of the book and establishing unified notation and terminology. After this standard spectral results for (bounded linear) operators on Banach and Hilbert spaces including the classical partition of the spectrum and spectral properties for specific classes of operators are discussed. A study of the spectral theorem for normal operators follows covering both the compact and the general case and proving both versions of the theorem in full detail. This leads into an investigation of functional calculus for normal operators and Riesz functional calculus which in turn is followed by Fredholm theory and compact perturbations of the spectrum where a finer analysis of the spectrum is worked out. Here further partitions involving the essential spectrum including the Weyl and Browder spectra are introduced. The final section of the book deals with Weyls and Browders theorems and provides a look at very recent results. Spectral Theory of Operators on Hilbert Spaces is addressed to an interdisciplinary audience of graduate students in mathematics statistics economics engineering and physics. It will be useful for working mathematicians using spectral theory of Hilbert space operators as well as for scientists wishing to harness the applications of this theory.