This lecture explores the limits of the Brillouin function, focusing on situations with very large total angular momentum and when the ratio of magnetic energy to thermal energy is much smaller than one, known as the Langevin and Curie law limits, respectively. The Langevin function is used to describe superparamagnetic behavior in materials with large magnetic moments, while the Curie law provides a simple way to understand the magnetic state of a system, with the susceptibility diverging at zero temperature.