The correct approach to the formulation of a new basis of quantum theory and new foundations of theory of atom is proposed. The unity of formal logic and rational dialectics is the correct methodological basis of the approach. The main result is the following principles: (1) the principle of motion of quantum particle; (2) the principle of stability of quantum particle; (3) principle of energy of quantum particle; (4) the principle of speed of translational motion of quantum particle; (5) the principle of rectilinearity of the external (translational) motion of quantum particle; (6) the principle of mass of quantum particle; (7) the principle of acceleration and of deceleration of quantum particle; (8) the principle of translational motion of electron in atom: the translational motion of electron in atom represents the periodical "scattering" of the electron by nucleus; (9) the principle of translational motion of electrons in many-electron atom: the translational motion of electrons in many-electron atom does not lead to formation of the electron shells. The proposed foundations furnish the clue to correct description of reality.