The advancement of electromagnetic engineering has been driving the need to develop efficient techniques for the transient analysis of transmission, propagation and reception of electromagnetic waves in different media. This book addresses a new method based on the numerical inversion of Laplace transform (NILT), which overcomes the restrictions in previous approaches, leads to good accuracy in both late and early time, and has simple algorithms, short calculation time and small required memory sizes. To our knowledge, this would be the first time that systematically treats the theory of NILT and its application in the transient analysis of electromagnetic waves. This book places the emphasis on how to extend and apply this method to a variety of cases. The correctness and effectiveness of this work are validated through the comparisons between our results and those published in the literature. Meanwhile, the results that cannot be achieved with the previous approaches are also provided. Moreover, this book presents some applications of the new technique in diverse engineering fields, including ultra wideband technology and material science.