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The paper is split into two major parts: (1) the first is to look into the EM wave properties in metamaterials and to develop an efficient solvers for their designs; and (2) the second is to try to design the metamaterials for antenna applications. For the efficient algorithms developed, the integral equation solvers accelerated using the adaptive integral (equation) method (AIM) and also the pre-corrected fast Fourier transform (pFFT) technique were developed and various examples in the designs will be demonstrated. In the second case, a single antenna designed using the metamaterial properties is considered, designed, fabricated, and measured. It is shown that the new design of the metamaterial antenna has a low loss (or high gain) and a broad bandwidth and this was never achieved using the conventional technique. The development of the metamaterial antennas was further extended to an array antenna and some interesting and promising results will be provided.