Filled with new approaches and basic results connected with the discontinuities of the electromagnetic field, this new book offers an important resource for graduate and undergraduate students. The discontinuities in question may be one of three things: The bounded jump discontinuities on the interfaces between two media or on the material sheets which model very thin layers or; Unbounded values at the edge of wedge type structures; Unbounded values at the tips of conical structures. The book contains many examples as well as problems and exercises that challenge the readers.