{it Elements of Operatory Theory} is aimed at graduate studentsas well as a new generation of mathematicians and scientists who needto apply operator theory to their field. Written in a user-friendlymotivating style, fundamental topics are presented in a systematicfashion, i.e., set theory, algebraic structures, topologicalstructures, Banach spaces, Hilbert spaces, culminating with theSpectral Theorem, one of the landmarks in the theory of operators onHilbert spaces. The exposition is concept-driven and as much aspossible avoids the formula-computational approach.Key features of this largely self-contained work include:* required background material to each chapter* fully rigorous proofs, over 300 of them, are specially tailored tothe presentation and some are new* more than 100 examples and, in several cases, interestingcounterexamples that demonstrate the frontiers of an important theorem* over 300 problems, many with hints* both problems and examples underscore further auxiliary results andextensions of the main theory; in this non-traditional framework, thereader is challenged and has a chance to prove the principal theoremsanewThis work is an excellent text for the classroom as well as aself-study resource for researchers. Prerequisites include anintroduction to analysis and to functions of a complex variable, whichmost first-year graduate students in mathematics, engineering, oranother formal science have already acquired. Measure theory andintegration theory are required only for the last section of the finalchapter.

1 Set-Theoretic Structures.- 2 Algebraic Structures.- 3 Topological Structures.- 4 Banach Spaces.- 5 Hilbert Spaces.- 6 The Spectral Theorem.- References.