The objective of this course is to explain  the mathematical methods used in  computational antenna  analysis and to provide students  with mathematical  background necessary for advanced  antenna engineering and electromagnetic software  development. This course can also serve as a  mathematical introduction to other ESoA courses.  The course will cover different approaches to solving  wave  equations, various wave representations, and  mathematical theorems used to simplify the original electromagnetic problem. In this sense, the aim of this course is to help students gain a deeper understanding of which field representation is suited for a given complex electromagnetic problem.