In this work, a new mechanics is proposed, based on a fundamentally new concept - the concept of an accelerated body and an accelerator body. The new mechanics is built in the form of the principles of interaction of two bodies. The principles are based on the universal laws of conservation of energy and momentum, and therefore apply to all types of matter. Newtonian mechanics is the generally accepted foundation of all modern physics. But it is only a simplified version of the new mechanics, and therefore cannot solve some fundamental problems of natural science. New mechanics describes physical phenomena more accurately, and therefore simply and naturally reveals the nature of phenomena of fundamental importance, for example, vibrational and translational resonance, resonance in the microcosm, the principle of relativity, the principle of least action, the first and second principles of thermodynamics, the foundations of quantum mechanics. Finally, even Newtonian mechanics itself is naturally “derived” from the new mechanics as its special case. This work is proposed as a modern universal physical and mathematical tool for solving practical problems that are insoluble within the framework of currently available physical concepts.