The paper gives a new definition of the motion of matter of two types, uniform and uniformly accelerated. Two fundamental new laws of motion are presented, on which are based all types of motion of matter in space Just as every form is inextricably linked with content and is in dialectical unity with it, space and time are inextricably linked with matter how in its state of rest and in its movement. In this sense, the concept of empty space without a material environment has no physical meaning. Thus, the subject of research in this paper was new applied forms of motion of material objects, for further research of the motion of matter in any form and in any moving inertial systems. It is impossible, without a deep revision of the accumulated knowledge in many areas of physics and mathematics of motion of material objects, the study of the motion of matter in any moving inertial systems, what is the fundamental object of study of the general theory of relativity The author has devoted many works 20,21,22 to this goal in his scientific research, outlining a new special theory of relativity. But the new general theory of relativity required an even deeper scientific and historical analysis of fundamental questions of physics, one of which is the motion of matter in rest systems, which is what this work is dedicated.