The book is devoted to the description of physical effects caused by resonant scattering of quasiparticles by isolated impurity atoms, which can localize electrons and phonons in nanosystems. It takes as its starting point the model of local perturbations by I.M. Lifshits, within which short-range impurity atoms are located at random points of the system. The role of a single impurity center in such systems increases with decreasing size. This book presents the first-ever application of the method of local perturbations to describe the physical properties of a wide range of nanosystems.