This book provides the theory, mathematics and computational tools that are necessary to model each and every one of the processes associated with lightning discharges. This is essential information for a newcomer to the subject as well as for experienced scientists working in this field. Indeed, it is only through exercising various models and mathematical simulations that one can understand the basics mechanisms associated with the generation and interactions of the electric and magnetic fields of thunderclouds and lightning. This book would appeal to undergraduate and post graduate Physics and Engineering Students, Lightning Protection and EMC Engineers and those working within the areas of Electrical Engineering, Computer engineering and Physics. This book provides the rules and computations procedures to bridge this physical understanding with high level computational procedures to model each and every electromagnetic process, whether static or dynamic, and their effects and interactions. This book makes it possible for the reader to apply the knowledge gained from these books such as The Lightning Flash, IET 2003 and Lightning Protection, IET 2010 and obtain first hand experience through simulations on the processes generating the electromagnetic field of thunderclouds and lightning flashes and the effects of these electromagnetic fields. They will also experience how the results described in these books will emerge when Maxwell's equations are combined with basic laws conservation laws of nature and physics of electrical discharges. Uniquely, the information provided in this book is not limited to lightning scientists and lightning protection engineers alone. The procedures used to study the interaction of lightning electromagnetic fields with structures, power lines and telecommunication systems can also be used to study the interaction of the said components with electromagnetic fields generated by any radio transmitter.