Technical systems experience fluctuations during operation, and their long-term safe operation requires that these fluctuations be predicted, assessed and analyzed to see if they do not adversely affect stability. This course provides a theory of equilibrium stability, as well as a revision of technique for constructing differential equations of motion. Free and forced oscillations of rods, shafts, beams, simple oscillations of discs, plates and shells, vibration of rotors and finally non-linear cases of oscillations are considered.