The microwave antenna is an ever active area of research because of its never ending demand in the modern communication systems. The microstrip patch antennas (MPAs) are well known due to their advantages such as low fabrication cost, light weight, low volume and also support both linear as well as circular polarization. On the other hand, MPAs suffer from the narrow bandwidth, single frequency resonance, and large size. However, due to the advancement of sophisticated technologies, the antenna designs need to be more compact and structure should shrink to fit smaller areas. Therefore there is an increased demand for miniaturized antennas for robust communications using industrial scientific and medical (ISM), wireless local area network (WLAN), Worldwide interoperability for microwave access (Wi-MAX) bands for wireless and airborne radar systems. Design and analysis of unit MNG and ENG MTM cells and extraction of constitutive parameters are worked out. Multiband antennas are also worked out in this thesis using the single layer as well as double layer RIS.