"Waves called solitons" is a technical book that explores the theory and applications of solitons in various physical systems. In its third edition, the presentation of new topics has been intentionally kept simple to enhance pedagogical accessibility. The book covers a wide range of aspects, including magnetic envelope solitons, signal processing with solitons, and the modeling of blood pressure pulses. It also provides insights into mechanical transmission lines and the properties of kink solitons, as well as compact waveforms known as compactons. The new chapters and sections expand the understanding of nonlinear lattice models and energy localization, while also addressing the concepts of self-trapped states and intrinsic localized modes. This comprehensive presentation makes the book a valuable resource for students and professionals interested in the dynamics of solitons and their applications in physics.