> What is the equivalent of "law 101"?
Many universities teach a course called "introduction to law."
> My naive understanding is that a lot of law studies are country specific.
And in the United States, they are state-specific, too!
> Is there some common set of principles that transcend the nation state and are useful for any inhabitant of the early XXI century to have on their pocket?
> I am imagining something like the concept of inflation, the role of central banks and monetary policy in economics.
Basically: no. In the West, Plato. In the anglophone West, John Locke probably qualifies, as well as Hobbes, some Bentham and Mill... or skip straight to Rawls. In China, Confucius. Some might say you could read Marx or Foucault, "power dynamics" might arguably transcend cultures in a generalized way, but I wouldn't bet on it.
> Or, If you wanted to understand how different law systems in the world work and the philosophical principles that they emanate from, then this set of fundamental concepts will help you to cut through the complexity. Some fundamentals...
Philosophy and political science majors often end up in law school, those are places where you'll find the "fundamentals" of jurisprudence. But the actual practice of law is often much more rhetorical, depends heavily on reputations, connections, and networks of contacts, and most lawyers don't learn anything about how to actually practice law until their first day on the job. In the 21st century, most lawyers are more like social technicians than they are like philosophers.