INTRODUCTION:Transcranial magnetic stimulation (TMS) has become an important tool for the study of the functional organization of the human brain as well as for the potential treatment of central nervous system diseases such as depression. The principles of localized magnetic stimulation, field calculations and functional brain mappings obtained by TMS, nerve excitation models, and applications for cognitive neuroscience are reviewed. In addition, the effects of repetitive TMS (rTMS) on the protection or recovery of injured hippocampal neurons in rats are discussed. Localized Magnetic Stimulation: TMS is a technique to stimulate the brain by magnetically induced eddy currents through a coil positioned on the surface of the head [Barker et al., 1985]. Mapping studies are carried out by a method of localized and vectorial magnetic stimulation using a figure eight coil [Ueno et al., 1988]. The basic principle is to concentrate induced eddy currents locally near a target by a pair of opposing pulsed magnetic fields produced by a figure-eight coil. When a transient current flows through a coil exterior to the head, time-varying magnetic fields are generated in the brain. The time -varying magnetic fields induce eddy currents that stimulate nerve fibers. When a single coil is used, the induced eddy currents flow in a concentrated manner. The maximum current density is attained beneath the coil and, in principle, the current density is zero at the center. When a figure-eight coil is used, flow patterns of induced currents create two vortices that merge at the point beneath the intersection of the figure-eight. A computer simulation shows that the current density at the merging point is three times greater than that in the surrounding areas. Hence, localized stimulation is attained. For TMS of the human brain, transient magnetic fields in the order of 1 T and a duration of 0.1-0.2 ms are generally used. These transient magnetic fields contribute to the depolarization of nerve cells in the brain. This method facilitates stimulation of the motor cortex of the human brain within a 5 mm resolution [Ueno et al., 1989; Ueno et al., 1990]. Vectorial stimulation can be attained because the concentrated eddy currents at the target under the intersection of the figure eight coil flow parallel to the tangent of the two circular coils. Based upon this principle, functional maps of the human motor cortex related to the hand, arm, and foot areas were obtained by measuring the motor evoked potentials (MEPs) of the peripheral muscle responses to the TMS. The functional maps showed that an optimal direction of stimulating induced currents for neuronal excitation exists in each functional area of the cortex. These vectorial characteristics in TMS reflect, in part, anatomical and functional organization of the neurons and neuronal fibers of the brain [Ueno et al., 1991]. Nerve Excitation Models: The introduction of nerve excitation models has widened our understanding of the mechanisms of nerve excitation elicited by magnetic stimulation...