Modern science of fluctuations and waves is presented in the book by its effects and phenomena found in medicine, chemistry, ecology, hydrodynamics, electronics, economics, social and other sciences. The aim of the book is to show that concepts such as vibrations and waves, instability and non-linearity, chaos and structures make it possible to understand the unity of the modern world picture. The book also shows how the ideas associated with these concepts penetrate into different sciences. Particular attention is paid to chaos and structures - central themes of synergy. The book is of independent interest, but can be considered as a continuation of D.I.Trubetskov’s book Introduction to synergy. Fluctuations and Waves» (М.: УРСС, 2003). The book can be useful for students of physical and mathematical classes, students of the first courses of natural sciences specialties of universities. The book was based on lectures given by the author at the Saratov State University to humanitarians. Therefore, the book can be interesting and useful for a wide range of readers interested in synergy.