This book is aimed at students who show a particular inclination towards Mathematics and want to lay a strong foundation of knowledge and skills from an early stage, with the ultimate goal of successfully pursuing advanced studies in the natural sciences.

A key motivation and strong incentive for serious and more systematic engagement with Mathematics is participation in the Thales, Euclid, and Archimedes competitions, which are 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 the international competitions, namely the Balkan Mathematical Olympiad and the International Mathematical Olympiad.

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

Special effort has been made to ensure 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, the authors have provided new solutions, while often we present, before the solution, thoughts and observations that methodically introduce the student to the approach of tackling them.