This study analyzes the Greek-Turkish dispute on the continental shelf over the Aegean Sea. In considering the Turkish claim on the Aegean Continental shelf, it was necessary to start with the historical reality of the Aegean, which refers to the real facts and events as they occurred from the past 3,000 years, from the origin of the Aegean to the present. This research shows that according to the ancient historians, philosophers and Geologists the Greek nation lived there from the dawn of history. The Aegean is the cradle of Hellenism. The sovereign and exclusive rights on the continental shelf over the Aegean Sea legally belong to Greece, according to the Treaty of Lausanne in 1923, Treaty of Italo-Turko in 1932, the Treaty of Montrex in 1936, Geneva Convention of 1958, the law of the Sea Convention of 1982, and the rules of International Law.