In 988, High King Mael Seachlainn II led the initial Irish conquest of the Norse Kingdom of Dublin, giving the place its modern name in Irish—Baile Átha Cliath, meaning "Town at the Hurdle Ford." Thus, the founding of Dublin is counted from the year 988, notwithstanding a village has existed on the site of Dublin since before the Roman occupation of Great Britain nearly a thousand years earlier.
Mael Seachlainn II was dethroned by Brian Boru, 1002-1014, and the Norse kept fighting back—so the Irish conquest of Dublin was never complete. Irish dominance of Dublin did take hold in the middle of the eleventh century, under the kings of Leinster; but the city still had a Norse king until the Norman invasion of 1171, and native Ireland itself was in the throes of the regnal wars over the high kingship since the death of Mael Seachlainn II in 1022. Though the last Norse king of Dublin was killed by the Normans in 1171, the population of the city retained their distinctiveness based on their origins for some further generations.
(N.B. "Sitric" is the Irish variant of Norwegian "Sigtrygg")