The collection contains over a thousand problems in elementary mathematics, mainly of increased difficulty. Tasks, if possible, are systematized and provided with solutions. In some cases, in connection with the solution of the problem and where appropriate, questions of theory are given. Sometimes they are sent to solve a group of problems united by a common idea. Explanations are given on the theory of equivalence of equations, plotting, complex numbers, inverse trigonometric functions, mathematical induction and some other issues.