The Biot–Savart law giving the vector potential A of a magnetic field B in terms of B is obtained. Structural properties of the general magnetic field are described, and magnetic helicity is introduced together with its topological interpretation in terms of flux-tube linkages. Simple mechanical examples of chiral behaviour are described. Toroidal/poloidal decomposition is defined and exemplified for axisymmetric and two-dimensional fields.The multipole expansion of the exterior field produced by a confined current distribution is obtained. Laws governing force-free fields are obtained, and particular force-free fields having field lines in the form of torus knots are described. The Lagrangian description of a magnetic field in a moving conductor is introduced, and the field evolution equation based on Faraday’s Law of Induction and Ohm’s Law is obtained. The free decay modes of a field in a spherical geometry are described, and the possibility of diffusive increase of the dipole moment is indicated. Fields exhibiting Lagrangian chaos are described. The notions of writhe and twist for knotted flux tubes are introduced, and the relation between helicity and writhe-plus-twist is explained. The behaviour when a flux tube passes through an inflexional configuration is explained.