An external magnetic field has different consequences on the properties of a solid, either by coupling to orbital degrees of freedom or spin degrees of freedom. Assuming the existence of magnetic moments, we consider the thermodynamic and statistical properties of various paramagnetic systems, both classical and quantum. Also, the magnetic permeability tensor is obtained and nonreciprocal systems are briefly mentioned. The classical Hall effect is considered in the semiclassical approximation, and the related effect of an anomalous velocity that originates from the topology of the electron bands is discussed. The case of high magnetic fields leads to electronic Landau levels and to the quantum Hall effect. The integer quantum Hall effect is discussed and its relation to topological considerations, and the existence of a non-vanishing Chern number of the bands is treated. The significant case of graphene is discussed, as well as the existence of a non-trivial Chern number in the Haldane model, where no magnetic field is required. The fractional quantum Hall effect is discussed qualitatively using the Laughlin wave function and the mapping to a classical system of charges in a given potential. Explanations of the phenomenology include composite fermions, the existence of fractional charges, and fractional statistics.