Short answers, pulled from the story.
International law is the set of rules, norms, legal customs, and standards that states and other actors feel obligated to follow in their mutual relations. Unlike domestic law, it lacks a centralized enforcement authority; compliance is driven by reciprocity, reputation, economic sanctions, and in some cases coercive action including diplomacy or military force.
The term "international law" was coined by Jeremy Bentham in his 1789 book Introduction to the Principles of Morals and Legislation, replacing the older term "law of nations."
The Peace of Westphalia, concluded in 1648, is considered the seminal event in the development of international law. It established the principle of Westphalian sovereignty, under which independent nation states are considered equal and sovereign regardless of size or power, with a corresponding norm of non-interference in domestic affairs.
Dutch jurist Hugo Grotius (1583-1645) is widely regarded as the father of international law. His 1625 work De Jure Belli ac Pacis laid down a system of natural law principles that he argued bound all nations regardless of local custom or law.
The International Criminal Court (ICC) was established by the 1998 Rome Statute as the first permanent international court to prosecute genocide, war crimes, crimes against humanity, and the crime of aggression. It has 123 state parties, but has been criticized by African countries including The Gambia and Kenya for "imperialist" prosecutions, and the United States declared in 2002 that it did not intend to become a party.
Article 38(1) of the Statute of the International Court of Justice lists four sources: international treaties, customary international law, general principles of law recognized by most national legal systems, and, as a subsidiary source, judicial decisions and the teachings of prominent legal scholars.