Nanoplasmonics is one of the most important growth areas of this century. It is part of nano-optics and nanophotonics and deals with oscillations of electrons in metallic nanoparticles and nanostructures. Also, it is a multidisciplinary subject covering atomic, molecular, and solid-state physics, as well as much of chemistry. Nanoplasmonics makes it possible to combine the nanoscale properties of smart devices with their optical frequencies of operation. Nanoplasmonics presents, for the first time, both the physical principles and mathematical descriptions of main nanoplasmonic effects that now are scattered over thousands of research articles. Importantly, it contains many methods, accompanied by diagrams, for fast estimations and calculations of main properties of nanoparticles of very different shapes and their clusters. It also presents the most important applications of nanoplasmonics, including in medicine, nanolasers, electronics, perfect lenses, and invisibility cloaks.