Which battle in 1066 led to Norman rule in England?

The Battle of Hastings, fought in October 1066 near the Sussex coast, gave England to William of Normandy. The crisis began with the death of Edward the Confessor without an heir, leaving three claimants: Harold Godwinson, who was crowned, Harald Hardrada of Norway, and William, who insisted he had been promised the throne. Harold destroyed the Norwegian invasion at Stamford Bridge in Yorkshire, then marched his army the length of the country in about a fortnight to meet William, who had landed in the south. At Hastings the English held a ridge in a shield wall that repeated Norman charges could not break, until parts of the line broke ranks to pursue apparently retreating Normans and were cut down in the open. Harold was killed. William's conquest replaced the English landholding class almost entirely and reshaped the language, law and architecture that followed.

The Domesday Book, compiled twenty years later, was William's survey of who held what land and what it was worth.