Short answers, pulled from the story.
The first Caspian raid occurred sometime in the reign of Hasan ibn Zaid, ruler of Tabaristan between 864 and 884. The Rus' sailed into the Caspian Sea and unsuccessfully attacked its eastern shore at Abaskun.
A fleet of 500 ships launched the first large-scale raid in 913 to attack regions including Arran, Tabaristan, Beylagan, and Shirvan. The Rus' plundered these areas taking women and children as slaves before being attacked by Khazars and Burtas on their return journey through the Volga Delta.
The second large-scale campaign is dated to 943 when Igor was prince of Kievan Rus'. The city of Bardha'a was saved only by an outbreak of dysentery among the Rus', which reduced their numbers and forced them to leave by night carrying treasure and captives.
Sviatoslav destroyed the Khazar capital of Atil probably in 968 or 969 after destroying the city of Sarkel around 965. This destruction brought prosperity and independence of Khazaria to abrupt end and paved way for Kievan Rus' to dominate north-south trade routes through steppe and across Black Sea.
In 1042 Ingvar the Far-Travelled led unsuccessful large Viking attack against Persia with fleet of 200 ships containing around 15, 20 thousand men. Legendary saga Yngvars saga víðförla describes last expedition dated to 1041 possibly connected with Georgian-Byzantine Battle of Sasireti.