Primer on Hilbert Space Operators by Piotr Sołtan.

Spectrum of an operator -- Continuous functional calculus -- Positive operators -- Spectral theorems and functional calculus -- Compact operators -- The trace -- Functional calculus for families of operators -- Operators and their graphs -- z-transform -- Spectral theorems -- Self-adjoint extensions of symmetric operators -- One-parameter groups of unitary operators -- Appendices -- Index of notation -- References - Index.

The book concisely presents the fundamental aspects of the theory of operators on Hilbert spaces. The topics covered include functional calculus and spectral theorems, compact operators, trace class and Hilbert-Schmidt operators, self-adjoint extensions of symmetric operators, and one-parameter groups of operators. The exposition of the material on unbounded operators is based on a novel tool, called the z-transform, which provides a way to encode full information about unbounded operators in bounded ones, hence making many technical aspects of the theory less involved.