The present textbook contains a consistent exposition of the foundations of the linear theory of oscillations and waves. Starting with a simple linear oscillator, we consider successively complicated theoretical models: an oscillator under external influence, associated oscillators and an environment from oscillators, wave kinematics and instability, waves in heterogeneous environments. The presentation is illustrated by examples from physics, chemistry, biology, economics. Along with this, there is a mathematical apparatus used in the linear theory of oscillations and waves. For students and graduate students of physical and physico-technical specialties of universities, as well as for researchers interested in the theory of oscillatory and wave processes