The premise of the show is showing different versions of Edmund Blackadder from varied time-periods, most of these incarnations are extremeley selfish, cynical and at times capable of malice - however like many anti-heroes he avoided becoming a complete monster by the fact that he fought against people worse than himself (that is, when villainous characters other than himself appeared of course..).
In his first incarnation, he is the youngest son of the fictional King Richard IV and the Duke of Edinburgh. Edmund is also the great-nephew of King Richard III whom he accidentally kills at the Battle of Bosworth Field. This resulted in Richard IV becoming King. Since he is not held in high regard by his father, Prince Blackadder's aim is to become King of England. He recruits some followers named the 'Six Most Evil Men in the Kingdom', who then betray him to Blackadder's rival, Philip of Burgundy. As a result, Blackadder is tortured and badly mutilated. His minions Baldrick and Percy poison the wine which is fed to Philip and his men but unwittingly poison the whole batch of wine. As a result, the royal family are poisoned. Blackadder, who is finally King, drinks the wine and dies. This makes him a tragic villain. This version of Blackadder is the closest to Edmund from King Lear.
The second incarnation of Blackadder was Lord Blackadder, a courtier to Queen Elizabeth I. Lord Blackadder has a rivallry with fellow courtier Lord Melchett and they fight over who gets to be the Queen's favourite. This incarnation of Blackadder saw him as vain and selfish, but he was able to defeat villains such as the Bishop of Bath and Wells. While he foiled Prince Ludwig's plan, Ludwig got the better of Blackadder and killed him.