The book presents proof of the independence of the continuum hypothesis from the other axioms of set theory - one of the most interesting and striking results obtained in mathematics over the past decade. It was for this result that its author, a professor at Stanford University P. Cohen, was awarded the Fields Medal at the last International Congress of Mathematicians (Moscow, 1966). The book will undoubtedly be of interest to a wide range of mathematicians, primarily specialists in set theory, mathematical logic and the foundations of mathematics. It will be useful for teachers, graduate students and senior students of universities and pedagogical institutes .