The Russian edition of the present book was published in June 2013. It just happened that it was the time between two significant dates: in 2011 the Nobel Prize was awarded ``for the discovery of the accelerated expansion of the Universe through observations of distant Supernovae'' and in 2013 the Nobel Prize was awarded ``for the theoretical discovery of a mechanism that contributes to our understanding of the origin of the mass of subatomic particles''. Both these formulations left the questions about the explanations of these phenomena in the framework of the fundamental principles open. Our book is devoted to attempts to explain the observed ``long distances to the Supernovae'' and ``the small value of the Higgs particle mass'' by the principles of affine and conformal symmetries and the vacuum postulate. Both these phenomena are described by quantum gravity in the form of joint irreducible unitary representations of the affine and conformal symmetry groups. These representations were used in our book to classify physical processes in the Universe, including its origin from the vacuum.