The name of Archimedes has long been synonymous with greatness in mathematics, yet few possess a clear understanding of why that is. This brochure aims to enlighten a broad audience with a basic mathematical background about his contributions. It does not claim to cover the entirety of Archimedes' work, nor does it seek to delve deeply into his genius. However, I believe it offers valuable insights into the mind of a man who paved the way for the great creators of modern mathematics and mechanics. Two thousand years have passed since he met his end, pierced by the sword of a Roman soldier, yet his vision of uniting theoretical research in mathematics with practical applications remains not only relevant but increasingly recognized today, guiding the endeavors of all forward-thinking scholars.