As another example of ordered phases, we consider magnetic phases in quantum systems. We start with a discussion of the origin of exchange energies between neighboring atoms through a brief discussion of the hydrogen molecule and the Wigner and Lieb and Mattis theorems. Various types of magnetic order in magnetic insulators are considered such as ferromagnets, ferrimagnets, and antiferromagnets. The low-temperature excitations of these magnetic systems are considered, using both a semiclassical approach and a quantum description, through the Holstein-Primakoff transformation. The case of magnetism in conductors is also considered, leading to the Stoner theory for itinerant magnetism. As a basis, we use the Hubbard model and treat it using the quantum equations of motion method to calculate the magnetic susceptibility to identify the magnetic instability and the ordered phase itself, showing the existence of Goldstone transverse modes. The case of strong local repulsive interactions between electrons in the context of the Hubbard model is shown to be related to the t-J model, where a mixture of electronic (charge) degrees of freedom and magnetic (spin) degrees of freedom is explicitly considered.