Metameterials, which are the subject of this dissertation, are used to obtain so-called "effective" media, such as media with negative index of refraction. Through a technique called transformation optics, metamaterials have also led to the design of invisibility cloaks. The field of metamaterials continues its rapid growth. One of the difficulties these applications face is dispersion, i.e.,the dependence of the electromagnetic properties of metamaterials on the frequency. In this dissertation, we use strong dispersion to our advantage for the design of a filter. We succeeded in applying techniques from electronic filter design to metamaterials in order to design a fourth-order low-pass Chebyshev filter for microwaves. This is demonstrated through finite-element simulations in the frequency domain and supported by a good agreement with theoretical models. The method for designing this filter may be scalable to terahertz and optical frequencies.