Short answers, pulled from the story.
Gaius defined ius gentium as what natural reason has established among all peoples. This definition separated the law of nations from civil law that applied only to Roman citizens.
Cicero described this unwritten law as a higher moral obligation binding human beings beyond specific state requirements. Stoic philosophy influenced the view that these rules were innate in every human being.
Hermogenianus listed wars, kingship, property boundaries, and commerce within the law of nations framework. These commercial contracts facilitated trade between different groups without requiring full citizenship.
Isidore enumerated principles focusing on peace treaties including occupation, construction, fortification, wars, captivity, slavery, and treaties. His work included the inviolability of ambassadors and prohibitions against mixed marriages.
The authority of the Pope declined while colonialism created subject nations outside Western Europe. European powers began constructing separate legal systems that ignored previous commonalities.
Rawls drew his concept of the law of peoples directly from traditional ius gentium with specific reference to the phrase ius gentium intra se meaning the law of peoples within themselves. He examined how modern states might function under principles derived from ancient Roman definitions.