The Book deals with the theory and application of a novel Scaled Boundary Finite Element Method in Computational Electromagnetics. The novel method was initially developed in the year 1997, for solving problems in the field of Elastodynamics. It was initially developed in Swiss Federal Institute of Technology, Lausanne, by Prof. John. P. Wolf and Chongmin Song.In this book, the theory behind the reformulation of the novel method suitable for solving Maxwell''s equations is dealt with in detail. As a consequence, a semi-analytical scaled boundary Finite Element procedure is developed to deal with electromagnetic problems,and which can be implemented numerically. The method combines the advantages of the Finite Element and Boundary Element methods.