The term "soliton" was coined only in 1965, to reflect the particle-like nature of solitary waves that remain intact even after mutual collisions. The book includes the latest developments in the field, including the main properties of erupting solids, considering the case of optical fiber systems described by the complex Ginzburg-Landau equation (CGLE); the propagation of ultrashort solitons in fiber-optic systems in the presence of intrapulse Raman scattering; the connection between rogue waves and modulation instability; the properties of solitary waves in coupled electrical nonlinear transmission lines, the results of experimental observations of solitary waves and their interactions, the engineering applications based on the management of solitary waves on coupled NLTLs; and finally, the effects of inhomogeneous exchange within ferromagnetic insulators.