The theoretical treatment of a cavity resonator consists of solving the Maxwell equations in that cavity, respecting the boundary conditions. The resonance frequencies appear as conditions in the solutions of the differential equation involved and are not significantly affected by the fact that the cavity walls have a finite conductivity. Solutions for rectangular cavities and for the lowest resonant mode, where the probability of mistaking one mode from another is slight, are readily obtained. The measurement of the complex permittivity, epsilon* = epsilon '-epsilon '', can be made using the small perturbation theory. In this method, the resonance peak frequency and the quality factor of the cavity, with and without a sample, can be used to obtain the complex dielectric permittivity of the material. We measure the shift in the resonant frequency of the cavity, Delta f, caused by the insertion of the sample, which can be related to the real part of the complex permitivitty, epsilon ', while the change in the inverse of the quality factor of the cavity, Delta(1/Q), gives the imaginary part, epsilon ''. In this work we report the construction details, the performance tests of the cavity to confirm the possibility of the use of the small perturbation theory, and the application of the technique to measure the complex permittivity of a reinforced plastic.