This book deals with the subject of optical and electronic negative refraction (NR) and negative index materials NIM). Diverse approaches for achieving NR and NIM are covered, such as using photonic crystals, phononic crystals, split-ring resonators (SRRs) and continuous media, focusing of waves, guided-wave behavior, and nonlinear effects. Specific topics treated are polariton theory for LHMs (left handed materials), focusing of waves, guided-wave behavior, nonlinear optical effects, magnetic LHM composites, SRR-rod realizations, low-loss guided-wave bands using SRR-rods unit cells as LHMs, NR of electromagnetic and electronic waves in uniform media, field distributions in LHM guided-wave structures, dielectric and ferroelectric NR bicrystal heterostructures, LH metamaterial photonic-crystal lenses, subwavelength focusing of LHM/NR photonic crystals, focusing of sound with NR and NIMs, and LHM quasi-crystal materials for focusing.