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Abstract The book contains a comprehensive account of the theory and application of neutron scattering for the study of the structure and dynamics of condensed matter. All the principal experimental techniques available at national and international neutron scattering facilities are covered. The formal theory is presented, and used to show how neutron scattering measurements give direct access to a variety of correlation and response functions which characterize the equilibrium properties of bulk matter. The determination of atomic arrangements and magnetic structures by neutron diffraction and neutron optical methods is described, including single-crystal and powder diffraction, diffuse scattering from disordered structures, total scattering, small-angle scattering, reflectometry, and imaging. The principles behind the main neutron spectroscopic techniques are explained, including continuous and time-of-flight inelastic scattering, quasielastic scattering, spin-echo spectroscopy, and Compton scattering. The scattering cross-sections for atomic vibrations in solids, diffusive motion in atomic and molecular fluids, and single-atom and cooperative magnetic excitations are calculated. A detailed account of neutron polarization analysis is given, together with examples of how polarized neutrons can be exploited to obtain information about structural and magnetic correlations which cannot be obtained by other methods. Alongside the theoretical aspects, the book also describes the essential practical information needed to perform experiments and to analyse and interpret the data. Exercises are included at the end of each chapter to consolidate and enhance understanding of the material, and a summary of relevant results from mathematics, quantum mechanics, and linear response theory, is given in the appendices.