The origin and properties of the transverse non-reciprocal magneto-optical (nMO) effect were studied. The transverse nMO effect occurs in the case when light propagates perpendicularly to the magnetic field. It was demonstrated that light can experience the transverse nMO effect only when it propagates in the vicinity of a boundary between two materials and the optical field at least in one material is evanescent. The transverse nMO effect is pronounced in the cases of surface plasmons and waveguiding modes. The magnitude of the transverse nMO effect is comparable to or greater than the magnitude of the longitudinal nMO effect. In the case of surface plasmons propagating at a boundary between the transition metal and the dielectric it is possible to magnify the transverse nMO effect and the magneto-optical figure-of-merit may increase from a few percents to above 100%. The scalar dispersion relation, which describes the transverse MO effect in cases of waveguide modes and surface plasmons propagating in a multilayer MO slab, was derived.The magneto-optical (MO) effect is important for a variety of applications. The effect is utilized to read data in a MO disk driver 1 , to switch an optical beam in optical switches 2 and to modulate light intensity in spacial light modulators 3 . It is a powerful scientific tool to determine the local magnetization of a material, to study the bandgap structure and spin-orbit interaction in a solid 4 . A unique feature of the MO effect is nonreciprocity. The optical properties of non-reciprocal devices are different for two opposite directions of light propagation. The non-reciprocal effect can occur only in a MO material and the important optical non-reciprocal devices such as an optical isolator and an optical circulator can only be fabricated by utilizing the MO materials.The MO effect is known to occur in a configuration when light propagates along a magnetic field. When the magnetic field is applied to a material, the electrons with spin directed along and opposite to the magnetic field have different energies. Since the electrons of one spin direction interact with light either of left or right circular polarization 5-7 , light of the left and right circular polarizations experiences different refraction and absorption. When light is transmitted through a MO material, there is a difference of refractive indexes (Faraday effect) and optical absorption (magnetic circular dichroism (MCD effect)) for left and right circularly polarized light. When light is reflected from a MO material, the reflectivity of the right and left circular polarized light is different (polar and longitudinal Kerr effects). All above-mentioned effects have the same origin and the similar properties and will be referred as longitudinal MO effects.It should be no MO effect in the case of the magnetic field applied perpendicularly to the light propagation direction. Since an electromagnetic wave is transverse, its polarization should be in a plane, which is perpendicular to the light propagation direction...