The purpose of the monograph of the famous physicist and mathematician Roger Penrose is to search for the fundamental principles underlying our universe and control the processes occurring in it. We can say that this book, in fact, is devoted to the relationship between mathematics and physics, the interaction between the two disciplines, which plays an important role in the desire to move on in search of a better theory to describe the universe. A specialist from any field will find something useful in this fundamental monograph; Perhaps the author’s point of view on some subjects differs (and sometimes quite radically) from the generally accepted, but this will allow us to look at the current problems of modern science from different angles and get closer to the truth. Of undoubted interest is his opinion on a number of modern theoretical constructions. These , for example, The Theory of Supersymmetry , Cosmology of the Expanding Universe , hypotheses about the nature of the Big Bang and black holes , String theory or M-theory , Cycle variables in quantum gravity, Twistor theory , Fundamental principles of quantum theory[edit] The book will cause undoubted interest both among specialists in natural sciences and among a wide range of readers.