The accurate analysis of waveguide discontinuities is an important problem in microwave communications. The objective of this three part work is to analyze the scattering properties of various types of waveguide discontinuities. In the first part, the general theory of rectangular waveguide, and the various numerical methods for computing scattering parameters of both the E-plane and H-plane waveguide discontinuities are discussed. The second part of the work presents the method of obtaining the scattering parameters of H-plane discontinuities and cascaded H-plane discontinuities using Mode Matching Technique (MMT) and Equivalent Circuit approach. In the third part of the work, MMT is extended to a new field analysis code based on a combination of MMT and Method of Moments called the Coupled Integral Equation Technique (CIET). CIET is applied to analyze circular corrugated waveguide discontinuities. It was found that CIET plays a major role in improving the performance by its efficient handling of singularities and in achieving accuracy.