There were several Caspian expeditions of the Rus in the course of the 10th century. The Yngvars saga víðförla describes what was the last Viking campaign in the Caspian in 1041, adding much legend to the historical facts. This expedition was launched from Sweden by Ingvar the Far-Travelled, who went down the Volga River into the land of the Saracens (Serkland). While there, they apparently took part in the Georgian-Byzantine Battle of Sasireti.
There are no less than twenty-six Ingvar Runestones, twenty-four of them being in the Lake Mälaren region of Uppland in Sweden, referring to Swedish warriors who went out with Ingvar on his expedition to the Saracen lands, an expedition whose purpose was probably to reopen old trade routes, now that the Volga Bulgars and the Khazars no longer proved obstacles. A stone to Ingvar’s brother indicates that he went east for gold but that he died in Saracen land.
A second theory suggests that Ingvar was the son of a Swedish prince named Eymundr and who would have been the son of Eric the Victorious and the brother of Olof Skötkonung. The existence of this prince Eymundr has been suggested by Lauritz Weibull (1911) and J. Svennung (1966). The theory is based on a reevaluation of the age of the Ingvar runestones, proposed by Elias Wessén and Sune Lindquist and which suggests that the Ingvar Runestones were carved earlier in the 11th century.
According to a third theory, proposed by F. Braun, and which is based on the runestones U 513, Rimbo.jpg, U 540, Sö 179 and Sö 279, Ingvar was the son of the Swedish king Emund the Old, and the grand-son of Olof Skötkonung. Emund the Old would have had two wives, Tola and Ragnhildr. Tola would have been the mother of Haraldr of Sö 179, and Ragnhild would have been the mother of Önundr, Eiríkr, Ragnarr and Hákon of the runestones U 513 and U 540. Önundr would be Anund Gårdske, who was raised in Russia, Eirík would be one of the two pretenders named Eric, Hákon would be Håkan the Red and Ingvar, Ingvar the Far-Travelled.
Ingvar's origin was, however, debated as early as the saga writers, or to put it in the words of Oddr Snorrason:
The participants were evenly distributed along the husbys, and 24 of the 26 Ingvar Runestones were from Sweden (in the contemporary sense, i.e. Svealand) and 2 from the Geatish district of Östergötland. The folkland of Attundaland did not take part and this was probably done on purpose in order to keep a defensive army in Sweden, while the main force was away.
Anund Jacob was the brother of Ingegerd Olofsdotter who was married to Yaroslav I of Novgorod and who conquered Kiev in 1019 from his brother Sviatopolk. This was done with the help of Varangians, and according to Ingvar's saga, they were led by Ingvar's father Eymund.
Later Yaroslav had trouble with the Pechenegs, a nomad tribe. The expedition stayed for a few years in Kiev fighting against the Pechenegs, then (in 1042) they continued to the Black Sea and the Christian country, called Särkland (Georgia).