Ch. 1. Operators of Linear Systems -- 1. Dynamic Compliance -- 2. Periodic Green Functions -- 3. Parametric Periodic Green Functions -- Ch. 2. Strongly Nonlinear Single-Degree-of Freedom Systems -- 4. Conservative Systems -- 5. Forced Vibration -- 6. Vibration in Autonomous Systems -- 7. Parametric Vibration -- 8. Random Vibration -- Ch. 3. Multiple-Degree-of-Freedom Systems -- 9. Forced Vibration in Multiple-Degree-of-Freedom Systems -- 10. Parametric Vibration in the Multiple-Degree-of-Freedom Systems -- App. I. The Averaging Method in Systems with Impacts -- App. II. On the Analysis of Resonant Vibration of Vibro-impact Systems Using the Averaging Technique -- App. III. Structure-borne Vibro-impact Resonances and Periodic Green Functions -- App. IV. Nonlinear Correction of a Vibration Protection System Containing Tuned Dynamic Absorber