Amber's legal system is feudal and aristocratic in nature. The essence of law is that a man (which is to say, the king) is rightful owner of all lands and property beneath him. He delegates this authority to his underlings, who have similar authority in turn, and so on down the chain. At its basic level, law is "Whatever the guy in charge says it is, so long as no one above him contradicts it."
Now, naturally such a system cannot last long in a pure state. Conflicts arise, disagreements must be resolved, power must change hand. A set of traditions and rituals emerge over time, shaped by rulings and circumstance. Men of power delegate more specific authority to handle day to day matters, and a class of men emerge to deal with the complexities and nuances that these matter produce. Much is recorded, but only some is codified in the sense a modern citizen would imagine it to be. Laws and rules exist so that things go the way the king wants them to, or as well as that can be approximated, in his absence - in his presence they are barely necessary.
Since Amber has had only one king, this produces an interesting schism. On one hand, no laws pertain to the king. His every word is law, and the body of law is the record of his word. After this long, even with occasional trimming by Oberon himself, the royal record is enough to fill a small library.
This is cumbersome and frequently contradictory, but it (combined with the rights of the Great Families) provide the basis from which all subsequent law in amber has been created. Amber city, for example, has extensive laws, ordinances and codes which are necessary for its day to day functioning. Laws of trade, property, taxation and everything else have all been built upon this somewhat maddening foundation.
This has been the basis of a number of purges throughout Amber history, because every few generations a well-intentioned individual tries to make sense of the (constantly growing) body of law - which is to say Royal Record. It's a great sprawling mess, and it would be much more useful if it could be organized, categorized, sorted and generally cleaned up into something logical, useful and actually usable by human beings. Unfortunately, to do such a thing is to presume to speak for the king. This pretty much always ends badly.
The irony is that, so far as the king himself is concerned, these laws matter not at all. To attempt to apply law to the king is treason.
With a new king, this opens up a wide variety of interesting questions regarding the role of the royal record. Theoretically a new king can call for revisiting the record, but this is a sticky wicket. So much subsequent law is based on interpretation and derivation from this body of law that if it should be disrupted, much subsequent law in Amber would be rendered null and void and supreme authority would devolve back to old blood oaths and rulership, more or less putting supreme authority back into the hands of the throne and the nobility. This would be a gigantic blow to trade, as the various rights and protections of property that allow it to thrive would go down like a house of cards. All of which ignores the sheer disrespect this gives to the old king and the blow this strikes to royal authority. At the same time, it is a vast opportunity for change, if handled with care. While it is not the flashiest or most dramatic challenges facing a new king, it may ultimately prove the most long lasting.