Double negative (DNG) metamaterials, which have both negative permittivity and negative permeability, have attracted intensive interest in the last few years for their exotic properties, such as negative refraction, reversed Doppler effect, reversed Vavilov-Cerenkov effect, and the possibility of making perfect lens. Theoretical investigations and practical experiments are being well undergone by many research groups over the world. Applications are found in RF circuit design, antenna size reduction, resonance devices, etc.;As one of the most important building blocks, transmission lines have intensive applications in RF and microwave engineering, such as couplers, phase shifters, filters, and leaky wave antennas. By replacing the conventional dielectric materials with DNG medium, we found numerous interesting properties. The complete mode spectrum and dispersive behavior of DNG medium are different from their DPS counterparts. Complex surface modes are found to be existing in a grounded DNG medium slab. When applying DNG medium to dipole radiation, both horizontal electric dipole (HED) and horizontal magnetic dipole (HMD) exhibits greatly enhanced radiation pattern due to the slow attenuation of the complex modes on the interface. Microstrip line with DNG is also investigated. It has large attenuation in low frequency band which implies that it is a good candidate for leaky antenna. At higher frequency, the attenuation drops to zero and the propagation constant bifurcates.;The method of moment is one of the most successful and efficient approaches in solving integral equations. However, the internal resonance problem of integral equations has plagued solutions of integral equations. A well known example is the internal resonance existing in both electric field integral equation (EFIE) and magnetic field integral equation (MFIE) for PEC scatterers or penetrable scatterers.;In the second part of my presentation, we will introduce the concept of original resonance and model resonance, followed by numerical matrix resonance and right-hand-side (RHS) resonance. We will thoroughly study their subtle differences and give numerical examples. The errors in electric current and scattered field near the resonances are studied for both EFIE and MFIE in solving for scattering solution from a 2D circular cylinder.