In this thesis photonic crystals (PhC's) with periodically modulated permittivity were examined. Besides one dimensional (1D) polymer based PhC's, high permittivity ceramic 1D and 2D PhC's were constructed. Simulated and experimental transmissions in the microwave (MW) range, as well as band structure calculations, were compared. A discrepancy between experimental and simulation results emerges for crystals with higher permittivity at higher frequencies. Furthermore a new property, a complete omnidirectional gap, of a 2D PhC with a simple square lattice having a ratio rod thickness/lattice constant (s/a) = 0.533 and a permittivity of 90, was found. Findings in the MW range are scalable to all wavelengths and therefore PhC's have high application potential in the MW as well as the optical range (e.g. telecommunications). A significant miniaturisation and/or increase in efficiency of lasers, LED's, filters and waveguides are/is achieved. A future goal is therefore the displacement of integrated electronics by optoelectronic and optical circuits.