Introduction -- Angular momentum and related matters -- Electromagnetic radiation -- The structure of free atoms and ions -- Magnetic effects in atomic structure -- Groups and their matrix representations -- Complex ions -- Crystal-field theory and the weak-field coupling scheme -- The strong-field coupling scheme -- Paramagnetic susceptibilities -- Optical spectra and thermodynamic properties -- Paramagnetic resonance -- Appendices: 1. The elements -- 2. Tables -- 3. Summary of relevant parts of perturbation theory -- 4. The Hamiltonian for a charged particle in an electromagnetic field -- 5. Gauge invariance in perturbation theory -- 6. Atomic spectral parameters -- 7. Deductions from Wigner's formula -- 8. L.C.A.O. theory -- 9. Symmetry of the coupling coefficients for the octahedral group