This handbook contains a collection of reference papers which survey the many aspects of modern operator theory and its applications. It begins with sections exploring real and complex reproducing kernel spaces, indefinite inner product spaces, de Branges spaces, and linear systems theory. Multivariable operator theory, infinite dimensional analysis, and quaternionic and hypercomplex analysis are considered in the following parts. For this Second Edition, the material has been updated throughout these sections, and many new papers have been added. The remaining sections are entirely new and cover operators and function spaces of analytic functions; non-commutative analysis; operators and superoscillations; operators for quantum particles and fields; the Koopman operator; and analysis and spectral problems in materials science.