In this thesis the general Chebyshev filter synthesis procedure to generate transfer and reflection polynomials and coupling matrices were described. Key concepts such as coupled resonators, non-resonant nodes have been included. This is followed by microwave duplexer synthesis. Next, a technique to design dual band filter has been described including ways to achieve desired return loss and rejection levels at specific bands by manipulating the stopbands and transmission zeros. The concept of dual band filter synthesis has been applied on the synthesis of microwave duplexer to propose a method to synthesize dual band duplexers. Finally a numerical procedure using Cauchy method has been described to estimate the filter and duplexer polynomials from measured responses. The concepts in this thesis can be used to make microwave filters and duplexers more compact, efficient and cost effective.