This chapter provides introduction to the important method of contemporarymagneto-optics, the nonlinear Faraday effect. It starts with a theoretical backgroundlinking the nonlinearity of the effect with quantum coherences of atomic states. Thediscussion of methods enabling analytical and numerical calculation of nonlinearmagneto-optical rotation are given. Next, Essential aspects of a typical experimen-tal apparatus used for investigation of the effect are described. Finally, the most im-portant applications of the phenomenon are reviewed, such as in magnetometry, nu-clear magnetic resonance, magnetic resonance imaging, magnetic particle detectionand quantum-state engineering
