A review of vibrational mechanics - the developing section of nonlinear dynamics and the theory of nonlinear oscillations. It offers a general approach to the study of the effect of nonlinear mechanical systems. The book presents the mathematical apparatus of vibrational mechanics which is used to describe such nonlinear effects as the disappearance and appearance under vibration of stable positions of equilibrium and motions (attractors), the change of the rheological properties of the media, self-sychronization, self-balancing, the vibrational maintenance or deceleration (retardation) of the rotation of unbalanced routers, resonances in the motions of celestial bodies, vibrational displacement and shift, vibrational excitation of streams and the transportation of bodies in the fluid. The book considers the use of these effects in creating new vibrational machines, technologies, and also principally new materials ("dynamic materials"). The volume contains many results previously published only in Russian and therefore unknown to specialists in the West, and also a review of the results obtained by researchers after the book was first published in Russia