Danelaw
In 1013 when it became clear that it was only Brian Boru's military might, not any kind of allegiance, that was holding his islandwide kingdom together. When the lords of Leinster and the Viking King of Dubhlinn held a second revolt, this was accompanied by general anti-Boru discontent in the rest of Ireland. Boru had his armies despoil the Leinster countryside as far as the Wicklow mountains before laying siege to the city of Dubhlinn itself for 4 months. But the Vikings held out, and when they had not submitted by Christmas the weather forced Boru to retreat. Knowing Boru would return in the spring, angrier than ever, the Leinstermen and the Vikings spent the winter frantically rallying support from western Scotland and the Isle of Man and amassed an army in the city. Brian Boru did indeed return, with his armies, in 1014. The two armies met at Clontarf, a fertile plain with a Monastery to the north-east of Dubhlinn. The battle was extremely bloody with several thousand men killed and, in the event, Brian Boru's army won and most of the Vikings took to their boats and retreated to the Isle of Man. In legend, the Battle of Clontarf has become one of the most famous in Irish history because it is seen as part of a national struggle, marking the expulsion of the Viking invader. In reality, the battle actually marks the failed attempt by Leinster and Dubhlinn to assert their independence from Munster.
During the 11th century Dublin became an important aquisition for any King with eyes on the High Kingship and, by the end of the 1000's it had overtaken Tara to become the de-facto capital of the island. Dublin thrived and remained a wealthy trading city. Excavations in the 1970s at Wood Quay in Dublin found incredibly well-preserved remains of a thriving Hiberno-Viking city. The King of Connacht made his son the Lord of Meath in the early 1100's. In 1101, the King of Munster granted the fortress on the rock of Cashel to the church who promptly set up an Archbishop at the site. At this point there were four main Kingdoms in Ireland: Munster, ruled by the O'Brien dynasty, of whom Brian Boru was part; Connacht, ruled by the O'Connor dynasty; the Uí Néill (whose land was called Tir Eoghain), ruled by the Mac Lochlainn dynasty and Leinster, ruled by the Mac Murchada dynasty. From 1086 until 1114, the High Kingship was in dispute. King Muirchertach O'Brien of Munster was the most powerful, but King Domnall Mac Lochlainn of the Uí Néill .
After the Battle of Clontarf (1014) many of the Hiberno-Norse Vikings migrated to England and settled in the north-west, from the Wirral to the Lake District. In northern England, as a crude generalisation, the Pennine watershed represents the interface of the 'Norwegian' and 'Danish' Viking regions. The last major Viking battle took place at Stamford Bridge near York in 1066, but the threat of further Scandinavian invasion, with ambitions to conquer and rule, did not diminish until well after the Norman Conquest of 1066 and, in fact, under Canute/Cnut (c.994-1035) the realm had a Danish monarch and was part of an Anglo-Scandinavian empire.
The Europe-wide revivial in Monasticism saw new Monastic orders bring Irish establishments under their control. The Cistercians were the first of the medieval orders to set up in Ireland, when St Malachy set up an abbey at Mellifont in 1142. The Archbishop of Canterbury in England wanted to assert control over the Irish church, and set about establishing links with the church in the influential former Viking city of Dublin. However, when the Irish church was reformed, over the course of three synods at Cashel (1101), Ráth Breasail (1111) and Kells-Mellifont (1152), the church was organised under an Archbishop placed at St Patrick's monastery at Armagh, much to Canterbury's displeasure - although the church in Dublin remained under Canterbury's control for some further time. The Vikings had invaded Anglo-Saxon Britain on a far greater scale than they ever had in Ireland, completely obliterating and colonising the Christian Kingdom of Northumbria as well as East Anglia and large parts of Mercia (see a map before the Viking invasion). This area was called the 'Danelaw'. Over the next 150 years, the two regions merged to form a more coherent Anglo-Norse England, ruled mostly by Danish Kings.