This book is aimed at students who show a particular inclination towards Mathematics and want to establish a strong level of knowledge and skills from now on, with the ultimate goal of successfully pursuing higher studies in the natural sciences.

A primary reason and strong motivation for serious and more systematic engagement with Mathematics is participation in the Thales, Euclid, and Archimedes competitions, organized annually by the Hellenic Mathematical Society, as well as in the national competitions for selecting the mathematical teams that will represent our country in international competitions, such as the Balkan Mathematical Olympiad and the International Mathematical Olympiad.

The topics have been selected with particular care and high criteria from the international arena, so as to cover both the difficulty and the thematic mathematical fields that currently attract the attention of the Olympiads.

Special effort has been made so that the problems are coherent, interconnected, and follow a progression from the simpler or easier to the more difficult and complex. In many of these, new solutions have been provided by the authors, while we often present, before the solution, thoughts and observations that methodically introduce the student to the way of tackling them.

[Excerpt from the text of the preface]