This book deals with the mechanics of impacts and vibrations and mitigation of their effects. It brings the expressions for impacts and for velocity, displacement and force in various cases of braking or stopping, and pays attention to the fact that force impulses propagate in bodies only with limited velocity. Then, it shows how various materials respond to load, how they absorb energy and how they can fail. Further it describes technical means for impact energy absorption, such as bend parts, compressed shells, composites, air cushions and hydraulic shock dampers with constant deceleration. One chapter is devoted to vibrations and mitigation of their effects. Formulae are presented for free and forced vibrations, without or with damping, and attention is also paid to the transmission of forces into foundations and to kinematic exciting, appearing during a vehicle ́s ride on a wavy road. Also a dynamic absorber of vibrations is described and vibrations of a system of several bodies. More complex analysis needs numerical methods, such as the finite element method. The last chapter is devoted to the dimensional analysis and theory of similarity, which can spare work during the development of appliances for the damping of impacts and vibrations. The book contains explanatory examples, numerous figures and references.