Modern-day compensation law likely began in Britain.
During the Anglo Saxon period in British history, blood feuds were a common occurrence.
When a family member was killed or injured, the victim's family usually sought revenge on the family of the perpetrator (by killing or inflicting injury). And then revenge was sought by that family again and so on, thus creating an endless cycle of violence.
However the monarch saw that this was a problem and passed a law called the Weregild Law (or Weregeld as it is sometimes spelt). Under Weregild law, if you injured someone, you had to pay them compensation. Or if you killed someone, you had to pay their family compensation. This is believed to be one of the origins of the modern compensation laws that we have today.
There are, of course, various earlier cases of compensation being paid to to people throughout many civilisations. But it's believed that the first law of its kind didn't exist until the Anglo-Saxon Weregild laws in Britain.