Includes bibliographical references (pages 739-740) and index.

Sets, mappings, groups -- Metric spaces -- Linear operators in linear spaces -- Linear operators in normed spaces -- The extended real line -- Measurable sets and measurable functions -- Measures -- Integration -- Lebesgue measure -- Hilbert spaces -- L² Hilbert spaces -- Adjoint operators -- Orthogonal projections and projection valued measures -- Integration with respect to a projection valued measure -- Spectral theorems -- One-parameter unitary groups and Stone's theorem -- Commuting operators and reducing subspaces -- Trace class and statistical operators -- Quantum mechanics in Hilbert space -- Position and momentum in non-relativistic quantum mechanics.