This course focuses on the phenomenon of ferromagnetism. Ferromagnetism is a magnetically ordered state of matter in which atomic magnetic moments are parallel to each other, so that the matter has a spontaneous magnetization. Owing to ferromagnetism, some materials (such as iron) can be attracted by magnets or become the permanent magnets themselves. The phenomenon of ferromagnetism plays an important role in modern technologies. It is a physical basis for the creation of a variety of electrical and electronic devices, such as transformers, electromagnets, magnetic storage devices, hard drives, spintronic devices, etc. However, in the absence of external magnetic field ferromagnetism does not occur at any temperature. It occurs only below some critical temperature, which is called the Curie temperature. For different ferromagnetic materials, the Curie temperature has its own value. It should be noted that the phenomenon of ferromagnetism arises due to the exchange interaction, which tends to set the magnetic moments of neighboring atoms or ions parallel to each other. The exchange interaction is a purely quantum effect, which has no analogue in classical physics. In this course we shall try to understand the microscopic origin of ferromagnetism, to learn about its experimental appearing, magnetizing field, magnetic anisotropy, and quantum mechanical effect. We try to build a quantum mechanical theory of ferromagnetism. The course is aimed to graduate students wishing to improve their level in the field of theoretical physics.