History of the Vikings

Harald (Mophead/Finehair)Halfdanasson

Halfdan (The Mild)  (p44)
Halfdan the Black (p51)
Ragnhild  (p76 Heimskringla) (daughter of Eirik king of Jutland)
Svanhild (p76 Heimskringla) (Daughter of Earl Eyestan.)
Ashild  (p76  Heimskringla) (daughter of Hring Dagsson)
Snoefrith  (p50  Heimskringla) (Svasis daughtter)
Thora Morstrong (p91 Heimskringla) Harald now 70 yrs old

Halfdan the Red
Olaf Geirstatha-Alf (p76 Heimskringla) by Svanhild

Bjorn (p76 Heimskringla) by Svanhild, a  King of Vestfold, A Chapman/merchant. Son Guthroth.  Eirik Bloodyaxe demands taxes owing to thier father the king, they quattel, Eirik get's nothing, they fight many people die, incuding  Bjorn  left with most of the wealth north  This is later than Halfdan Heleggs and Halfdan the Whites death. Halfdan the black is upset with this, and burns down Eirik bloodyace hall down, with most of Eiriks men in it,  Eirik asleep in a barn neaarby. He escapes with four others and goes back to the king (next part- Halfdan the Black (not offisilly published this yet, so things will change as I learn)

Ragnar Rykill (p76 Heimskringla) by Svanhild
Eirik Bloodyaxe (p76 Heimskringla) by Ragnhild
Ubbi (p.71 Heimskringla)

Halfdan the White ???-870 Estonia  (p73 p83 Heimskringla) by Asa. Killed in Estonia

Halfdan the Black (p73 Heimskringla) by Asa
 Halfdan the Black, after burning down Eirik Blooyaxe's farm/Hall  Finds the kings fleet moored outside the Thorsfjord, and he places his fleet on the land side. Envoys try despute before coming to an agreement. Halfdan the Black keeps his province.(p 90-91 Heimskringla) 

Guthorm (p73 Heimskringla) by Asa  - Marshall of Vikings 

Dag (p76 Heimskringla) by Aschild
Hring (p76 Heimskringla) by Aschild
Guthroth Skirja (p76 Heimskringla) by Aschild
Inggigerth (p76 Heimskringla) by Aschild
Sigurth Hrisi (p50  Heimskringla) by Snoefrith 

Halfdan Halegg (Longshanks) (p50  Heimskringla) by Snoefrith. Burns down Earl Rognvold or Moer (Nederlands), burns down his house and 60 warriors, then steals 3 ships, set's off to the Hebredies (Isles North of Scotland).  Thorir put in charge (son of Rognvold). Finehair now in control of the Nederlands. The Hebredies are where Helgg met his death blood  Eagled 

Guthroth Ljomi (p50  Heimskringla) by Snoefrith 
Rogvold Rettibeini (p50  Heimskringla) by Snoefrith 

Hakon (p91 Heimskringla)  by Thora

Where Harald is concerned, he inheritedthe realm of Vestfold an a agressive aquition and disposition under  the regency of his Uncle 870-880 there abouts
 First he had to fend off rivals (he is a minor king at this time). There are many scores to be paid off against the memory of his father
Under his Uncles tutelage, Harald establishes himself in Vestfold and makes himsel Master of the neighbourin kingdon too. There is a quote here "The blood-red stem had takrn root (p53)
 Concerning the name Mophead After he had defeated most of his near rivals, he met a pricess called Gyda of Hordaland, she told him that she could not marry pett kingling who did not have a proper kingdum to his name, He swore not cut or comb his hair until he had subdued the whole of Norway. Eventually, he succeeded, and and Gyda was impressed enough to join him (along with the other wives and comcubines he had)
 On the meeting  Earl Rognvold clipped his hair, unclipped for 10 years says the Saga says, and the nickname became Finhair (They are said to have jet black hair).
 He managed to come to terms with Eaarl Hakon Grjotgarsson. 
 The Vestfold noy under contro He set about  taking the South West which was owned by a powerful Sea king known as Kjotvi the wealthy. A very important area now bounded bounded between Bergan and Stavanger.bit by bit from his home inTrondelag, he pushe furthr South beating any opperstion he came accross his path. The  moment came whem he had to meet his main rivals fleet at Hafrsfjord (West of  Stavanger). The battle one and it is said many a sea king met his death that day, he could truely call himself King of Norway.
 Magnus dates the battle at 890, but most beliieve  880-890. (So well after the 845 Raids of Ragnar and Horik).
 I think this battle was important,a as there would have been Norwegian attacks on Britain and France, as many involved in the raids of earlier years, are now deceased.

Source: Vikings by BBC host of Mastermind, Magnus Magnusson. (p = page number in that book I also checked the Hheimskringla, and put those page numbers up for you to check) 
External links & compilation  S. Broberg (I do my best to get the correct for you, but no guaranteees)