This book is aimed at high school students who have a special relationship with mathematics and the sciences in general. It is particularly useful for those students who participate in mathematics competitions, such as "THALES," "EUCLID," and "ARCHIMEDES," organized by the Hellenic Mathematical Society (H.M.S.). It also serves as a vast reservoir of knowledge for university students, mathematicians, and any other reader who appreciates and is fascinated by the beauty and applications of Mathematics.

The material is initially developed by grade and by chapter. For each chapter, important theoretical elements are provided, along with basic applications, followed by all the topics from the "THALES" and "EUCLID" competitions, which are accompanied by detailed solutions at the end of the book. Four sections in total are dedicated to the "ARCHIMEDES" competition. The final sections of each volume contain theory and applications from the most important areas of competitive mathematics. Finally, each book concludes with a series of selected topics from the preliminary competitions, which are held to select and form the national teams that will represent our country in international competitions.

This book is also an important tool for our country, contributing to the further dissemination of the competitive spirit and leading many students to seek and complete positive scientific thinking.