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Contents 1. Introduction . 2. Fundamental theory . 2.1. Cross-section formula . 2.2. Bragg condition . 2.3. Polarization dependence of the cross section 2.4. Nuclear interaction potential . 2.5. Magnetic interaction potential , 2.6. Spin-only scattering . 3. Small I K I approximation for magnetic scattering 4. Tensor operator approach , . . 4.1. The need for a new formalism . 4.2. Summary of properties of irreducible tensor operators 4.3. Structure of the cross-section expression 4.4. The neutron spin factor d 4.5. The crystal factor B . . . 5 . Matrix elements of the magnetic interaction operator 6. Dipole approximation , 6.1. Dipole approximation for an isolated ion . 6.2. Dipole approximation for the general case . 7.1. General structure of the formulae . 7.2. Algebraic structure of the formulae . 8.1. Terbium, Tb3+ , 8.2. Cobalt, Coz+ . 8.3. Uranium, U4+ .