Electromagnetic band-gap (EBG) materials, also known as photonic band-gap (PBG) materials or electromagnetic crystals (ECs), exhibit a forbidden range of frequencies, i.e., band gap across which electromagnetic wave cannot propagate. This thesis investigates an EBG structure, composed of multi-layer metallic open square rings (OSRs) structure and its application to novel microwave designs. The structure is studied in air and dielectric media. First, the operating principles (eigenmodes, dispersion diagrams and confined modes) are elucidated for an infinite layered structure in air media. The effects of OSR geometrical parameters on the band gap are investigated. A maximum width of band gap is obtained by judicious selection of the structural parameters of the EBG. Then, studies of finite layered structures such as EBG slabs and EBG slab line-defect waveguides are performed. It is shown that the number of guided modes at different frequencies are specified by the number of layers with defects. On the other hand, in absence of defects within the layers, guided modes cease to exist. Following these findings, detailed studies are conducted on EBG slabs and EBG slab line-defect waveguides in dielectric media. Similar modal behaviour has been observed for the EBG OSR structure in both media. In a first application, line defect EBG waveguides that are fed with integrated conventional microwave circuits are designed, fabricated and experimentally tested. Designs are developed to operate at Ku band (12-18 GHz) and acceptable agreement was found between simulations and measurements of the foam (air)-supported guide. Then, dielectric-supported guides are developed. Good agreement was also observed between theoretical and experimental results in X-band (8-12 GHz). In both EBG channel types, the insertion loss per unit length does not change significantly by increasing the length of the periodic channel. In a second application, novel layered OSR line-defect waveguide directional couplers capable of producing arbitrary coupling are designed. Quasi-0-dB couplers and 3-dB couplers are numerically demonstrated, with good phase balance, and isolation. Unique features of these couplers are wave propagation in the forward- and/or backward- directions that can be reconfigured by simply rotating coupling elements.