Among those noted by the Irish annals, the Chronicle of the Kings of Alba and the Anglo-Saxon Chronicle are Ívarr — Ímar in Irish sources — who was active from East Anglia to Ireland, Halfdán — Albdann in Irish, Healfdene in Old English — and Amlaíb or Óláfr.

Æthelstan's empire, seemingly made safe by the victory of Brunanburh, collapsed in little more than a year from his death when Amlaíb returned from Ireland and seized Northumbria and the Mercian Danelaw.

In 945, Edmund of Wessex, having expelled Amlaíb Cuaran ( Olaf Sihtricsson ) from Northumbria, devastated Cumbria and blinded two sons of Domnall mac Eógain, king of Strathclyde.

This battle is not reported by the Anglo-Saxon Chronicle, and it is unclear whether it should be related to the expulsion of Amlaíb Cuaran from York or the return of Eric Bloodaxe.

Amlaíb Cuarán succeeded him and did so with popular support, as the Anglo-Saxon Chronicle ( MS D ) reports that in 941, “ the Northumbrians belied their pledges, and chose Olaf Amlaíb Cuarán from Ireland as their king .” Amlaíb shared the throne with his nephew Ragnald ( Rögnvaldr ), son of Gofraid.

There was even a precedent for employing Norsemen from the isles ; they had been used by Sigtrygg's father, Amlaíb Cuarán, in 980, and by Sigtrygg himself in 990.

Cuilén was succeeded by Dub's brother Kenneth II ( Cináed mac Maíl Coluim ), who was driven from the throne for a short time in the later 970s by Cuilén's brother Amlaíb.

There is no contemporary evidence setting out the descent from Ímar to his grandsons, but it may be that the grandsons of Ímar recorded between 896 and 934 — Amlaíb Cuarán's father Sitriuc ( d. 927 ), Ragnall ( d. 921 ), Gofraid ( d. 934 ), Ímar ( d. 904 ) and Amlaíb ( d. 896 )— were brothers rather than cousins.

Amlaíb was expelled from the kingship of York in 944.

In 870 Dumbarton was besieged by Amlaíb Conung and Ímar, " the two kings of the Northmen ", who " returned to Dublin from Britain " the following year with numerous captives.

In the same source Amlaíb Conung is also recorded as having gone to the aid of his father Gofraidh, who was under assault from Vikings in Lochlainn in about 872.

Amlaíb committed treachery against Les Mór, and Martan was liberated from him.

Wimund may have been a member of the party sent from Furness to found a house at Rushen on the Isle of Man by request of Amlaíb son of Gofraid Cróbh bhan, the King of Mann and the Isles, in 1134.

The final entry deviates from the Irish kings and instead tells of the death of Amlaib ’ s son, Oistín and reads: “ Oistín son of Amlaíb, king of the Norsemen, was deceitfully killed by Albann .”

In 866 Amlaíb and Auslie left Ireland with the larger part of the Norse forces, and in cooperation with the Norse-gaels from present day Scotland they attacked the picts.

As a result, it has been suggested that Godred was a son, or nephew, of the Norse-Gael king Ímar mac Arailt who ruled Dublin from 1038 to 1046, who was in turn a nephew of Sigtrygg Silkbeard and grandson of Amlaíb Cuarán.

From Irish annals it is known that Edmund's old rival Olaf Guthfrithson left Dublin in 939 ( Annals of the Four Masters ), that in 940 his cousin Amlaíb Cuarán ( also Olaf Sihtricsson ) joined him in York ( Annals of the Four Masters, Annals of Clonmacnoise ) and that Olaf Guthfrithson died in 941 ( Annals of Clonmacnoise, Chronicon Scotorum ), while the Anglo-Saxon Chronicle ( MS E ) dates his death – incorrectly it seems – to 942.

The Irish annals report that in 945, Amlaíb was back in Dublin and an anonymous ruler at York, possibly Ragnald ( Rögnvaldr ), died.

In 870 an army led by the Viking chiefs known in Irish as Amlaíb Conung and Ímar laid siege to Alt Clut, a siege which lasted some four months and led to the destruction of the citadel and the taking of a very large number of captives.

After defeating a rival Norse king whose name is recorded in Old Irish documents as Amlaíb Cenncairech at Limerick in August 937, Olaf Guthfrithsson crossed the Irish Sea with his army to join the forces of Constantine and Owen, suggesting that the Battle of Brunanburh probably occurred in early October of that year.

Amlaíb was married at least twice, and had many children who married into Irish and Scandinavian royal families.

It was borrowed into Old Irish and spelled Amlaíb.

* Amlaíb Ua Donnubáin ( Auliffe O ' Donovan ), regional Irish king

The main figure in the revenge tales is Ivar, who is sometimes associated with the Viking leader Ímar, brother of Amlaíb Conung, found in the Irish annals.

The Old Irish form of these names is Amlaíb mac Gofraid.

This defeat appears to have lost Amlaíb his kingship, as the annals record that Blácaire not Amlaíb was the leader of the Dublin forces in the following year.

Some Viking individuals of note mentioned in the annals with parallels in other historical sources are the foreign chieftain Turgeis, beginning in 845, Ímar and Amlaíb, the later progenitors of the

It appears that after Æthelstan's died, not only did Edmund lose control of Northumbria, but that the Five Burghs of the Mercian Danelaw also pledged themselves to Amlaíb mac Gofrith.

While Edmund certainly controlled Northumbria after Amlaíb was expelled and Ragnall killed, he may soon after have lost control of the north to a Scandinavian king named Eiríkr, usually identified with Eric Bloodaxe.

While Amlaíb and Auisle were in north Britain, the Annals of Ulster record that Áed Findliath, High King of Ireland, took advantage of their absence to destroy the longphorts along the northern coasts of Ireland.

Eirik's removal cleared the way for Amlaíb Cwiran, who having suffered defeat at Slane ( Co. Meath, Ireland ) in 947, returned to Northumbria and took the kingship, supposedly in 949, if the E-text is to be trusted.

According to William of Malmesbury, Amlaíb fled to Ireland while his uncle Gofraid made a second unsuccessful attempt to gain control of York.

After being driven out of Northumbria, Amlaíb returned to Ireland while Ragnall may have been killed at York.

The course of events in Northumbria while Amlaíb was in Ireland is uncertain.

Amlaíb returned to Ireland, never again to rule in York.

Amlaíb Conung is described as the " son of the king of Lochlainn " in the Fragmentary Annals of Ireland and Ó Corráin ( 1998 ) argues that Lochlainn " is Viking Scotland and probably includes Man " at this time suggesting an early date for an organised Kingdom of the Isles.

Cynan ab Iago ( 1014 – 1063 ) was a Welsh Prince, the son of Ragnhilda of Ireland, daughter of Amlaíb mac Sitriuc, and Iago ab Idwal, King of Gwynedd and father of Gruffudd ap Cynan who also became king of Gwynedd.

" ( Ímar and Amlaíb are well-attested Norse leaders active in Ireland and the Isles in the 9th century.

Amlaíb and Auisle ( Ásl or Auðgísl ), said to be his brother, brought an army to Fortriu and obtained tribute and hostages in 866.

Late sources of uncertain reliability state that Auisle was killed by Amlaíb in 867 in a dispute over Amlaíb's wife, the daughter of Cináed.

In 870, Amlaíb and Ívarr attacked Dumbarton Rock, where the River Leven meets the River Clyde, the chief place of the kingdom of Alt Clut, south-western neighbour of Pictland.

Another son had died at Brunanburh, and, according to John of Worcester, Amlaíb mac Gofraid was married to a daughter of Constantine.

Eric Bloodaxe took York in 948, before being driven out by Edred, and when Amlaíb Cuaran again took York in 949 – 950, Máel Coluim raided Northumbria as far south as the Tees taking " a multitude of people and many herds of cattle " according to the Chronicle.

* King Kenneth II of Scotland kills Amlaíb, brother of King Culen, to establish himself as Culen's successor.

Óláf Sihtricson, otherwise known as Amlaíb Cuarán (' Sandal '), had been king of Northumbria in the early 940s, when he became Edmund's godson and client king, but he was later driven out.

An early suggestion is that the name for the king in York in the Life of Cathróe has been erroneously supplanted for Eric's predecessor Amlaíb Cuarán ( Olaf Sihtricsson ), whose ( second ) wife Dúnflaith was an Irishwoman.

The Orkneyinga saga, written c. 1200, does speak of Eirik ’ s presence in Orkney and his alliance with the joint jarls Arnkel and Erland, sons of Torf-Einarr, but not until his rule in Northumbria was challenged by Olaf ( Amlaíb Cuarán ).

In response, Amlaíb launched a successful raid on Tamworth ( Mercia ), probably sometime later that year.

However, in 943, when Amlaíb had marched on to Leicester, one of the Boroughs, he and Wulfstan were besieged by Edmund and managed to escape only by a hair's breadth.

Peace negotiations followed later that year to that effect that Edmund accepted Amlaíb as an ally and as two northern sources add, ceded to him Northumbria as far south as Watling Street.