Scattering neutrons produced by fission have a high range of energies. In a nuclear reactor, these neutrons are slowed down by scattering collisions with atomic nuclei until they are thermalized. In the thermal energy region, the neutrons exchange energy with the moderator atoms. Therefore, there is an up-scattering of neutrons such that neutrons gain energy, as well as the common down-scattering occurs and neutrons lose energy. As a result of various interactions, the neutron energies in a reactor core vary approximately from about 10 MeV to 0.001 eV. These energy ranges are divided into a finite number of discrete energy groups. Hence, we get multigroup neutron diffusion equations, which is the focus of this chapter. In the first section, some important information from the existing literature on the multigroup neutron diffusion equation is presented. Then, the formulation of the problem and a finite element procedure to solve these types of problems are explained in the second and third sections, respectively.