Which countries did the Vikings invade during the middle ages?

The Vikings originally came from three countries in Scandinavia; Denmark, Norway and Sweden. The name 'Viking' came from a language called 'Old Norse' and means 'a pirate raid'. People who went off raiding in ships were said to be 'going Viking'. The Viking age in European history was about AD 700 TO 1100. During this period many Vikings left Scandinavia and travelled to other countries, such as Britain and Ireland. Some went to fight and steal treasure. Others settled in new lands as farmers, craftsmen or traders. 

The Viking Age 700-1100

Year	What happened in that year
700 AD	The Viking age begins
787	The first Viking raid on England
793	Vikings attack monastery at Lindisfarne
865	The Great Army of the Vikings invades England
866	Vikings capture York
878	King Alfred defeats the Vikings
900	Vikings established a rule over the north of Scotland
1000	Vikings establish a short-lived settlement in North America
1001	Vikings land in America
1002	King of Sweyn of Denmark invades England
1016	Knut of Denmark becomes King of England
1066	William the Conqueror, who is descended from the Vikings, invades England
1066	The end of the Viking age

The Viking alphabet

Why did the Vikings used coins instead of bartering?

The Viking Age saw major changes in the economy of Scandinavia. At the beginning of the Viking age, very few people in Scandinavia had any knowledge of coinage. Some foreign coins entered the region because of trading contacts both with western Europe and the Islamic world to the east. However, except in major trading centres such as Hedeby and Ribe, in Denmark, the idea of coinage was unfamiliar. Coins were valued only for their weight in gold or silver, and circulated with many other forms of precious metals.
This is what is known as a bullion economy, in which the weight and the purity of the precious metal is what's important, not what form the metal takes. Far and away the most common metal in the economy was silver, although gold was also used. Silver circulated in the form of bars, or ingots, as well as in the form of jewellery and ornaments. For the Vikings, it was easier for them to carry coins because they migrated many times so instead of bartering for goods they made coins and used those.

These are some Viking coins found in Furness, North West England

These coins were also part of the find in Furness, North West England 

How do we know the Vikings were here?

The Vikings have left many traces of their settlement which are still visible today. Archaeology provides evidence of their adventures, settlement and their daily life. The study of their 
language shows the lasting effect that the Viking settlements had in the British Isles, and DNA analysis shows the effect the Vikings had on the genetics of the countries where they settled. All of this gives valuable information, but the only reason we have non idea of the 'Vikings' as people is their appearance in the drawings found by archaeologists.
http://www.dightonrock.com/thevikingsneverhadanaythingtodow.htm

The first findings of Viking artifacts were found in the early 1060's. The first recorded raid on Britain was in 789 (three ships raided Portland). The last raid attempt was Harald Hardrada's in 1066 which failed spectacularly. 

Archaeologist Patricia Sutherland (orange jacket) excavates a potential Viking site on Baffin Island.