This book starts with the basic idea of the eigenfunction expansion method and then goes on to describe the dyadic Green’s functions. It presents the method to analyze waveguide slot arrays with the method of moments and explains how to program in Matlab. This book describes the basics and applications through an example of the waveguide slot arrays.The eigenfunction expansion method described in this book is limited to those structures that are almost consistent with the rectangular coordinate system. However, since the electromagnetic field is analytically represented by the mode distribution inherent in the shape of the structure, the computation time is reduced. Since it is fast, many parameters can be designed in a certain amount of time in combination with optimization methods. Also, the waveguide slot arrays discussed in this book have low transmission loss if they have a hollow structure. Therefore, high antenna efficiency can be achieved even at high frequencies using a millimeter-wave and terahertz wave. I believe that the waveguide slot antennas can make a significant contribution to the 5th generation mobile communication, which has just begun, and to future wireless communication systems.