Explain the theories of immunity and the functional-necessity doctrine.

Immunity is jurisdiction's mirror: the rules by which one subject is excluded from another's jurisdiction — the device that lets equals interact (par in parem non habet imperium) and lets international functions operate. Three families (distinguish them in your opening paragraph): (i)representative immunities (diplomatic agents, consuls, special missions — the Vienna regime, treated in IRD Unit 6 and recapitulated here); (ii) state immunity (the sovereign state itself before foreign courts); (iii) functional immunities of international organizations and theirofficials. The theories: personal representation (the ambassador as the sovereign's embodiment), extraterritoriality, and — the modern doctrine — functional necessity (immunity as the guarantee of function: the VCDR Preamble's own logic).