A country XYZ is not a member of United Nations. A dispute arises between XYZ and its neighbouring country over territorial waters. XYZ wants to take the matter to International Court of Justice. Can it do so, as it is not a member of United Nations?

Yes, it can as Article 93 of the United Nations Charter allows the non members to approach it.

The International Court of Justice ('ICJ') is termed as the main judicial branch of the United Nations. In 1946, the General Assembly of the United Nations, enacted the Statute of the ICJ which gave rise to the institution of the International Court of Justice at The Hague, Netherlands. All members of the UN are party to this statute, by default owing to Article 93 of the United Nations Charter, and non-members may also become parties under this Article.

The court may also give advisory opinions under Articles 65-68 of the Statute of the ICJ to countries. These are not binding but are merely referrals to the ICJ to understand the point of law on the matter. The ICJ is thus, one of the primary sources of dispute resolution available with regards to international disputes when parties are agreeable to settle them on their own accord