The book is a collection of problems from elementary mathematics. It can be of substantial help in work with gifted secondary school students. On the other hand, it also contains problems on determinants, special sequences, functional equations, primitive functions, difference and differential equations, so that it will be useful for work with students of basic courses on analysis and algebra. The collection is divided into 24 groups. Over 100 problems are presented with solutions, and another 150 are accompanied by hints and clear ideas how to proceed on the way to a solution. Using included material, the author leads readers from active problem solving to exploration of methods to obtain new problems and to an active use of the gained inventive skills. The book is based on the author’s personal long lasting cooperation with the Romanian journal Gazeta Matematica.