The latest cosmological revolution began in 2015, when gravitational waves from the merger of many invisible black holes of stellar mass that make up the dark matter of space were discovered. This discovery led to the creation of a model of the oscillating Universe, in the dynamics of which gravitational radiation and black holes play a key role. This book describes for the first time a cyclic cosmology that explains the physical mechanism of the Big Bang and the modern acceleration of the expansion of the Universe (the phenomenon of a positive cosmological constant or “dark energy”). The main text of the book is written at a popular level, but the appendix contains a comprehensive mathematical description of the oscillating Universe with variable gravitational mass. The book is of interest to a wide range of readers, physics students and specialists.