Who are the four kings of the middle ages 1066-1500?

I am assuming you mean kings of England, since your question has the date 1066, which was pivotal in English history. There were many more than four kings of England. They included the following:

  • William I the Conqueror
  • William II Rufus
  • Henry I Beauclerc
  • Stephen who fought with Matilda, claiming to be king
  • Matilda, who claimed to be queen, but withdrew that claim after years of war
  • Henry II
  • Richard I the Lionheart
  • John Lackland
  • Henry III
  • Edward I Longshanks
  • Edward II
  • Edward III
  • Richard II
  • Henry IV
  • Henry V
  • Henry VI
  • Edward IV
  • Edward V
  • Richard III
  • Henry VII

The last of these reigned until 1509.

There is a link below to a list of English kings, starting at the entry for 1066. You can follow links from that article to articles on the individual kings.