Ferromagnetism and the Curie temperature were explained by Weiss in terms of a huge internal ‘molecular field’ proportional to the magnetization. The theory is applicable both to localized and delocalized electrons. No such magnetic field really exists, but it is a useful way of approximating the effect of the interatomic Coulomb interaction in quantum mechanics, which Heisenberg described by the Hamiltonian describing the localized spins on two adjacent atoms. When J > 0, ferromagnetic exchange leads to ferromagnetic order in three dimensions. Spin waves are the low-energy excitations of the exchange-coupled magnetic lattice. In the delocalized electron picture, a ferromagnet has spontaneously spin-split energy bands. The density of ↑ and ↓ states is calculated using spin-dependent density functional theory. Important physical phenomena associated with ferromagnetism are then discussed, including magnetic anisotropy, magnetoresistance, magnetoelastic and magneto-optic effects.