This text, based on lectures delivered over almost two decades, explains in detail the theory of linear Hilbert-space operators and its use in quantum physics. The central mathematical tool of this book, the spectral theory of self-adjoint operators, is used in a systematic analysis of the operator aspect of quantum theory. The authors wish to provide students with basic information about the field and, perhaps, to kindle interest that will lead to further research. This text is intended to be of use to students and teachers in all fields of physics who use quantum theoretical methods, as well as researchers in theoretical and mathematical physics and mathematicians with an interest in quantum theory.