Ingibiorg Finnsdottir (normalised Old Norse: Ingibjǫrg Finnsdóttir, Norwegian : Ingebjørg Finnsdotter) was a daughter of Earl Finn Arnesson and Bergljot Halvdansdottir.  She was also a niece of Kings Olaf II and Harald Hardrada of Norway.  She is also known as Ingibiorg, the Earls'-Mother.  The dates of her life are not known with certainty.
She married Earl Thorfinn Sigurdsson of Orkney. The Orkneyinga Saga claims that Kalf Arnesson, Ingibiorg's uncle, was exiled in Orkney after her marriage to Thorfinn. This was during the reign of Magnus the Good, son of Olaf II, who ruled from 1035 to 1047, and probably before the death of Harthacanute in 1042.  Thorfinn and Ingibiorg had two known sons, Paul and Erlend Thorfinnsson, who jointly ruled as earls of Orkney. Both also fought in Harald Hardraade's ill-fated invasion of the Kingdom of England in 1066.    
Ingibiorg remarried after Thorfinn's death (actual date unknown)  Her second husband was King Malcolm III of Scotland. Whatever the exact date of the marriage, Malcolm and Ingibiorg had at least one son, and probably two. The Orkneyinga Saga tells us that Duncan II (Donnchad mac Mail Coluim) was their son,  and it is presumed that the "Domnall son of Máel Coluim, King of Scotland" whose death in 1085 is reported by the Annals of Ulster was also their son. 
Ingibiorg is presumed to have died in around 1069 as Malcolm married Margaret, sister of Edgar Ætheling, in about 1070.  It may be, however, that she died before Malcolm became king, as an Ingeborg comitissa appears in the Liber Vitae Ecclesiae Dunelmensis, a list of those monks and notables from whom prayers were said at Durham, alongside persons known to have died around 1058.  If Ingibiorg was never queen, it would help to explain the apparent ignorance of her existence displayed by some Scots chroniclers. 
Malcolm III was King of Scotland from 1058 to 1093. He was later nicknamed "Canmore". Malcolm's long reign of 35 years preceded the beginning of the Scoto-Norman age. Henry I of England and Eustace III of Boulogne were his sons-in-law, making him the maternal grandfather of Empress Matilda, William Adelin and Matilda of Boulogne. All three of them were prominent in English politics during the 12th century.
The Orkneyinga saga is a narrative of the history of the Orkney and Shetland islands and their relationship with other local polities, particularly Norway and Scotland. The saga has "no parallel in the social and literary record of Scotland" and is "the only medieval chronicle to have Orkney as the central place of action". The main focus of the work is the line of jarls who ruled the Earldom of Orkney, which constituted the Norðreyjar or Northern Isles of Orkney and Shetland and there are frequent references to both archipelagoes throughout.
Saint Magnus Erlendsson, Earl of Orkney, sometimes known as Magnus the Martyr, was Earl of Orkney from 1106 to about 1115.
Malcolm IV, nicknamed Virgo, "the Maiden" was King of Scotland from 1153 until his death. He was the eldest son of Henry, Earl of Huntingdon and Northumbria and Ada de Warenne. The original Malcolm Canmore, a name now associated with his great-grandfather Malcolm III, succeeded his grandfather David I, and shared David's Anglo-Norman tastes.
Máel Coluim mac Cináeda was King of Alba (Scotland) from 1005 until his death. He was a son of King Kenneth II; but the name of his mother is uncertain. The Prophecy of Berchán says that his mother was a woman of Leinster and refers to him as Forranach, "the Destroyer".. In contrast, Frederic Van Bossen, a historian from the 17th century, who spent many years accessing many private libraries throughout Europe states his mother was Queen Boada, the daughter to Constantine and the granddaughter to an unnamed Prince of Norway.
Magnus Haraldsson was King of Norway from 1066 to 1069, jointly with his brother Olaf Kyrre from 1067. He was not included in official Norwegian regnal lists until modern times, but has since been counted as Magnus II.
Rognvald Eysteinsson was the founding Jarl of Møre in Norway, and a close relative and ally of Harald Fairhair, the earliest known King of Norway. In the Norse language he is known as Rǫgnvaldr Eysteinsson (Mǿrajarl) and in modern Norwegian as Ragnvald Mørejarl. He is sometimes referred to with bynames that may be translated into modern English as "Rognvald the Wise" or "Rognvald the Powerful".
Einarr Rognvaldarson, often referred to by his byname Torf-Einarr, was one of the Norse earls of Orkney. The son of the Norse jarl Rognvald Eysteinsson and a concubine, his rise to power is related in sagas which apparently draw on verses of Einarr's own composition for inspiration. After battling for control of the Northern Isles of Scotland and a struggle with Norwegian royalty, Einarr founded a dynasty which retained control of the islands for centuries after his death.
Thorfinn Torf-Einarsson also known as Thorfinn Skull-splitter was a 10th-century Earl of Orkney. He appears in the Orkneyinga saga and briefly in St Olaf's Saga, as incorporated into the Heimskringla. These stories were first written down in Iceland in the early 13th century and much of the information they contain is "hard to corroborate".
The Earldom of Orkney was a Norse territory ruled by the earls of Orkney from the ninth century until 1472. It was founded during the Viking Age by Viking raiders and settlers from Scandinavia. In the ninth and tenth centuries it covered the Northern Isles (Norðreyjar) of Orkney and Shetland, as well as Caithness and Sutherland on the mainland. It was a dependent territory of the Kingdom of Norway until 1472, when it was absorbed into the Kingdom of Scotland. Originally, the title of Jarl or Earl of Orkney was heritable.
Thorfinn Sigurdsson, also known as Thorfinn the Mighty, was an 11th-century Jarl of Orkney. He was the youngest of five sons of Jarl Sigurd Hlodvirsson and the only one resulting from Sigurd's marriage to a daughter of Malcolm II of Scotland. He ruled alone as jarl for about a third of the time that he held the title and jointly with one or more of his brothers or with his nephew Rögnvald Brusason for the remainder. Thorfinn married Ingibiorg Finnsdottir, daughter of Finn Arnesson, Jarl of Halland.
Sigurd Hlodvirsson, popularly known as Sigurd the Stout from the Old Norse Sigurðr digri, was an Earl of Orkney. The main sources for his life are the Norse Sagas, which were first written down some two centuries or more after his death. These engaging stories must therefore be treated with caution rather than as reliable historical documents.
Harald Maddadsson was Earl of Orkney and Mormaer of Caithness from 1139 until 1206. He was the son of Matad, Mormaer of Atholl, and Margaret, daughter of Earl Haakon Paulsson of Orkney. Of mixed Norse and Gaelic blood, and a descendant of Scots kings, he was a significant figure in northern Scotland, and played a prominent part in Scottish politics of the twelfth century. The Orkneyinga Saga names him one of the three most powerful Earls of Orkney along with Sigurd Eysteinsson and Thorfinn Sigurdsson.
Finnr Árnason was a Norwegian nobleman and advisor to both King Olaf Haraldsson and King Harald III of Norway and later served King Sweyn II of Denmark. He was the feudal lord (lendmann) of Austrått.
Brusi Sigurdsson was one of Sigurd Hlodvirsson's four sons. He was joint Earl of Orkney from 1014. His life is recorded in the Orkneyinga Saga.
Einar Sigurdsson, also called Einarr rangmunnr Sigurðarson or Einar Wry-Mouth, was a son of Sigurd Hlodvirsson. He was jointly Earl of Orkney from 1014. His life is recorded in the Orkneyinga Saga.
Rognvald Brusason , son of Brusi Sigurdsson, was Earl of Orkney jointly with Thorfinn Sigurdsson from about 1037 onwards. His life is recorded in the Orkneyinga Saga.
Paul Thorfinnsson and Erlend Thorfinnsson were brothers who ruled together as Earls of Orkney. Paul and Erlend were the sons of Thorfinn Sigurdsson and Ingibiorg Finnsdottir. Through Ingibiorg's father Finn Arnesson and his wife, the family was related to the Norwegian Kings Olav II and Harald II. They are both described as "tall, handsome men, shrewd and gentle, taking rather more after their mother's side of the family. Their lives and times are recounted in the Orkneyinga Saga, which was first written down in the early 13th century by an unknown Icelandic author.
Haakon Paulsson was a Norwegian jarl who ruled the earldom of Orkney together with his cousin Magnus Erlendsson from 1105 to 1123. Their lives and times are recounted in the Orkneyinga saga, which was first written down in the early 13th century by an unknown Icelandic author.
Karl Hundason, also Karl Hundisson, is a personage in the Orkneyinga Saga. The saga recounts a war between Thorfinn Sigurdsson, Earl of Orkney, and Karl, whom it calls king of Scots. The question of his identity and historicity has been debated by historians of Scotland and the Northern Isles for more than a century. However a literal translation suggests that the name may simply be an insult.