This key work analyses the disputes between Greece and Turkey as to their respective rights in the Aegean Sea, paying particular attention to the claims regarding territorial waters, the continental shelf, and the yet to be declared exclusive maritime zones in the area. While many earlier studies have concentrated on political factors, this study provides an exhaustive analysis of the relevant principles of international law in general and rules and principles of maritime law in particular, identifying the legal principles appropriate to the settlement of the Aegean dispute. With this regard, it makes a detailed examination of all the related aspects of the Aegean Sea and its islands, as well as the legal arguments of Greece and Turkey on the disputes concerned. It also clarifies the prospects for settling the dispute on the basis of international law, either by the two parties involved, or by the intervention of a third party such as the International Court of Justice. As such, it offers an important study of a particular problem, but one that can be used as a case study for other international disagreements.