Thirty UN Member States and the Provisional Institutions of Self-Government (PISG) of Kosovo, which authored the declaration of independence from Serbia in February 2008, are scheduled to speak during the hearings, which will run until 11 December.
Both Serbia and the PISG are slated to address the ICJ today.
In October 2008 the General Assembly voted to request the ICJ to give an advisory opinion on the legality of the move by Kosovo, where ethnic Albanians outnumber Serbs and other minorities by about nine to one.
The ICJ, also known as the World Court, is tasked with settling legal disputes between UN Member States and with giving advisory opinions on legal questions. It is based in The Hague in the Netherlands.