This paper develops a theory of DM in the current LCDM framework, whose main hypothesis is that DM is generated by the own gravitational field, according an unknown quantum gravitational phenomenon. The hypothesis of DM by quantum gravitation, DMbQG hereafter, has two main consequences: the first one is that the law of DM generation has to be the same, in the halo region, for all the galaxies and the second one is that the haloes are unbounded, so the total DM goes up without limit. The first one consequence is backed by the fact that M31 and MW has a fitted function with the same power exponent. The theory firstly is developed with M31 rotation curve data up to the chapter 10. The chapter 11 is dedicated to apply the theory to MW. The results of its direct mass are tested successfully using the data published at different radius. In the chapter 12 is calculated the direct mass for the L.G. The DMbQG theory is the only one able to calculate the total mass at 770 kpc that match with dynamical measures of mass. In the chapter 13 is shown a method to estimate the Direct mass formula for a cluster of galaxies, using its virial mass and radius. By this method it is estimated the parameter a2 of the L.G. , the Virgo and Coma. Chapter 14 shows how DE is able to counterbalance the DM, as the Direct mass grows up with the square root of radius whereas the DE grows up with the cubic power. This theory aims to be a powerful method to study DM in the halo region of galaxies and cluster of galaxies and conversely the measures in galaxies and clusters offer the possibility to validate the theory.