In my Final Project I mainly investigate the mathematical and electrical basis of inductive charging technologies. For the most part, I present the modeling methods and steps needed to be able to describe these systems. I start with a quick analysis of the internal combustion engine to show its relative worse efficiency. Then I demonstrate the transformer models. I use the methods of circuit analysis for the determination of the governing equations. I handle and solve them using complex algebra, and if optimum points are needed I either use differentials unless the choice is evident. The mathematics used manually can be summarized with these two branches of science. My final aim is the expression of transformer parameters as a function of their geometry. Eventually, every parameter for a given application will be quantized as a function of the turns, the cross-sectional areas and the frequency. The result is an algorithm that allows the optimal design of such an air-gap transformer. The interpolation and the calculations are carried out by computer. I used Wolfram Mathematica 9. Then I briefly write about technologies in general, this part doesn’t use math but rather gives an overview in their main application types. In the last part I run simulations using Matlab Simulink which support the results of my calculations.