During life, a person faces many different tasks.  Some of them turn out to be elementary, while others require serious thought.  Some problems, the conditions of which were formulated hundreds of years ago, have not yet been solved.  This book is a unique collection of the greatest challenges of the past and present.  While working on its creation, the author listened to the opinion of the scientific community: the publication includes only those problems that most experts consider the most important in mathematics.  Each of them is a kind of bifurcation point, on which the path of further development of science depends.