We have experienced the difficulty of many graduate students in understanding the equationsDiffusionequation related to ionic diffusion. The purpose of this chapter is to demonstrate these laws, which are of primary importance in characterizing the properties associated with ionic transport in solid electrolytes. The demonstrations of the formulas outline the approximations that determine the conditions under which they can be used. We start with Fick's laws to derive the diffusion equationDiffusionequation and theDiffusionNernst-Einstein equations Nernst-Einstein equationNernst-Einstein equations. The time dependence of the diffusion lengthDiffusionlength is demonstrated by the exact solution of theDiffusionrandom walk problem random walk problemRandom walk problem. We then study the fundamental laws of transport associated with theDiffusionhopping mechanism hopping mechanismHopping mechanism in crystals and the Vogel-Fulcher lawDiffusionVogel-Fulcher law in non-crystallized materials. A section is devoted to the calculation and measurement of the transfer coefficientDiffusiontransfer coefficient, as this parameter is important in determining the performance of polymer electrolytes in particular. A clear distinction is made between the ambipolarDiffusionambipolar and chemical diffusion coefficients determined by GITTDiffusionGITT. The GITT is a remarkable tool and attention is focused on how it can be used to determine the anionic and cationic partial conductivities in addition to the diffusionDiffusionNernst-Einstein equations coefficient.