In practice, jurisdiction is confused.
The nations in your atlas might seem to be clearly defined, but map publishers say that their national boundaries reflect de facto, not de jure, recognition; they show the region controlled by a government, without implying that it has a correct to that control.
The truth is that hardly any states are free of charge of territorial disputes.
Many states claim jurisdiction over quite distant places (dependencies, or colonies).
There are even disputes in between citizens of the same nation.
One region may have its own cultural identity, and wish to join a neighbouring country, or even to form a brand new state.
International law does not concern itself with solving disputes like this, even though they often end in bloody civil wars.
A quarrelling nation may sever diplomatic relations with its rival by bringing its ambassadors home.
It may damage a rival's trade by imposing taxes on goods that cross its territory.
It might even declare war.
Under worldwide law, peace is the 'normal' state of affairs between nations.
Various laws apply in wartime; these set limits for the fighting, specifying legitimate targets and fair treatment for prisoners.
There are also international laws covering neutrality; by agreement among fighting nations, certain states may remain off-limits to the conflict.
No police force can make a nation obey worldwide law, so some people say that it isn't law at all; it's a set of morals.
But most states do toe the line; worldwide laws are shown as much respect as domestic ones.