This will be the first book on the topic of new methods in inverse problems in electromagnetics. The inverse problems such as optimization, synthesis, diagnostics, and identification are becoming one of the most important subjects in the field because of the significant practical applications to electric circuits and electromagnetics. This book introduces the recent achievements in mathematics and computing. The information on how to use the modern theoretical ideas and methods to solve inverse problems will help both students and specialists. The book systematically treats modern mathematic methods of inverse problems solution by providing descriptions of the most important practical inverse problems and the methods to solve them. Included also are descriptions of the properties of inverse problems and known methods of their solution as well as the practical implementation of these methods in electric circuits theory and electromagnetic fields theory.