Zeroth Law of Thermodynamics

If two thermodynamic systems are both in thermal equilibrium with a third system, then the two systems are in thermal equilibrium with each other.

The name had always intrigued me. The third law of thermodynamics was established in 1912. Decades later, Ralph Fowler established a law that was considered to be more fundamental than all the previous ones. The law can not be stated more simply, but it's inference leads to the description of Temperature. Consider a mercury thermometer, it in itself is a system that has defined properties. A thermometer is able to reach thermal equilibrium with the system whose temperature is to be measured without influencing the properties of the system itself. If this thermometer is able to reach thermal equilibrium with two separate systems, then by the zeroth law, the two systems are also in equilibrium with each other. Being in thermal equilibrium with each other, these systems have the same thermal temperature.

I find this equivalence very cool, it establishes a metric based on just the relation of equivalence and nothing more. If we establish a direction of non-equilibrium, based on the direction of flow of heat, we define hot and cold. This addition of direction creates a heirarchy of temperature, based on the relation.