The Vikings were Indo-European people from Scandinavia (modern Denmark, Norway and Sweden), who began around the 400s AD to make frequent raids by boat into Europe, even going into the Mediterranean Sea and raiding Sicily and southern Italy. The Vikings began attacking the Atlantic coast of southern France around 400 AD, and also the eastern coast of England.
In 860 AD, another branch of Vikings migrated south into Russia to trade with Constantinople. A large Viking fleet attacked Constantinople in 860, and though they couldn't get past the walls of the city, they plundered many rich monasteries outside the walls. In Russia, the Vikings gradually mixed with the Slavs who were living there and founded the country of Russia. Together, the Slavs and the Vikings took their boats down the Dnieper river to the Black Sea, where they traded with people further east along the Silk Road like the Samanids. The Vikings sold furs and wool to the Samanids, and the Samanids sold the Vikings silk from China, and steel from India and Central Asia, which the Vikings took home and made into excellent swords to sell in Europe.
By 1000 AD, some of the Vikings settled in northern France, where they were called the Normans, or Northmen, and the area where they settled is still called Normandy. Here they also converted to Christianity, and Matilda and William built their churches. In 1066 AD, William and his Normans conquered England in addition to their holdings in France.
The Vikings and the Slavs kept on raiding the Roman territory around Constantinople, though they could not take the city itself. Soon the Byzantine Empire was hiring Vikings as soldiers. By 999 AD, there were Viking mercenaries fighting for the Lombards and the Byzantines in Italy. By 1050, they began to conquer south Italy for themselves. Many Viking men also fought for the Byzantines at the Battle of Manzikert between the Byzantines and the Seljuks over Armenia in 1071 AD. After losing the battle, these mercenaries revolted - perhaps hoping to get land for themselves as their friends had done in Italy - but this time Alexius Comnenos defeated them. Not long afterwards, in 1096 AD, the Vikings returned to Constantinople as the First Crusade. Alexius helped them get to Jerusalem, where they established a new kingdom. By 1151, the Normans controlled all of southern Italy and the island of Sicily, and were making repeated attacks on Greece, sometimes building castles there.
Not all the Vikings went east, though. At around the same time, some Vikings sailed west to Iceland, Greenland, and even as far as Nova Scotia, in modern Canada. Some Viking men married Native American women there. The Vikings settled in Iceland and Greenland, but only stayed in Canada for a short time, because the Inuit people there were too strong for them, and because a global cooling period beginning about 1300 AD made the oceans too icy for their ships.
Eyewitness: Viking, by Susan M. Margeson and Peter Anderson (2000).
You Wouldn't Want to Be a Viking Explorer!, by Andrew Langley and others (2000).
Make This Viking Settlement (Usborne Cut Out Models), by I. Ashman (1998)
The Vikings: 350 Years of Adventure to Unlock and Discover (Treasure Chests), by Fiona MacDonald (1997).