I am by no means an expert on Viking history or early Nordic history, but I'd suggest checking out:

Brink, Stefan, ed. The Viking World (2008). A book which combines many short chapters on any topic relevant to Vikings or the Scandinavian late Iron Age.

The Vikings by Else Roesdahl. It gives quite a comprehensive history for anyone looking to get into the period.

I also suggest checking out this reading list on Viking history & culture. It's all quite introductory, so it should be fine for what you want it for.

I remember answering a similar question:

Here is the link: http://www.reddit.com/r/AskHistorians/comments/1yi821/i_would_like_to_learn_more_about_vikings_is_there/

My answer on that thread was as follows:

I am sure /u/Ninja_Please117 can inform you about some of these books that I have listed off. As I am sure they probably looked at some when I suggest them to them.

When I was taking Viking Raiders to Crusaders at Trinity College I came across some books that were helpful. I hope this puts you in the right direction, and that these books are what you are looking for.

I think this will count as more as enough places to start. Let me know if you want more. I have more as well. Most of these sources especially the ones I used on my paper (bibliography section) are excellent books with tons of content.

I guess with the Vikings it is also best to clarify that I find the term to be a catch all. An overview is a really broad subject band in my opinion.

Happy reading.

Peter Hunter Blair: An Introduction to Anglo-Saxon England

Gwyn Jones: A History of The Vikings

Andrew Wawn: The Vikings and the Victorians: Inventing the Old North in Nineteenth-Century Britain

National Geographic - Vesilind, Priit J: In Search of Vikings. National Geographic; May2000, Vol. 197 Issue 5, p2, 26p, 21 Color Photographs, 1 Map

P.H. Sawyer: Kings and Vikings: Scandinavia and Europe AD 700-1100

D.O. Corrain: Ireland before the Normans

Bibilography of a paper I wrote: Byock, Jesse. The Saga of the Volsungs: Richard Wagner and the Saga of the Volsungs. Berkeley: University of California Press, 2001.

Clements, Jonathan. A brief history of The Vikings: The last pagans or the first modern Europeans?. London: Constable & Robinson ltd, 2005.

Haywood, John. Encyclopaedia of the Viking Age. London: Thames & Hudson, 2000.

Klæsøe, Iben Skibsted . Viking Trade and Settlement in continental Western Europe. Copenhagen: Museum Tusculanum Press, 2010.

Richards, Julian. The Vikings: A very short introduction, (New York: Oxford University Press Inc, 2005).

Quaife, Milo. "The Myth of the Kensington Rune Stone: The Norse Discovery of Minnesota." The New England Quarterly. 7. no. 4 (1934).

Wahlgren, Erik. The Kensington stone: a mystery solved. Madison: University of Wisconsin Press, 1958.

Wawn, Andrew. The Vikings and the Victorians: Inventing the Old North in Nineteenth-Century Britain. London: D.S. Brewer, 2000

The Penguin Historical Atlas of the Vikings is an excellent little compilation of maps about the Vikings. Don't be put off by the cover: this is a great companion for visualising various viking journeys, although it is quite short.

Vikings! by Magnus Magnusson is a 1980s summary of archaeological knowledge of the vikings. It is not comprehensive, because it is about 30 years out of date. It is, however, highly readable and still pretty good at giving a broad impression. I found it invaluable for finding out about archaeology of the viking age: other people will have other opinions.

The Prose Edda, with the penguin translation by Jesse Bycock (different translations and publishers present the edda very differently!) was, I found, a short, highly enjoyable, and above all very readable introduction to the basics of norse literature. It is in some ways to Norse mythology what 'Genesis' is to Christian mythology: a source for many of those small details elsewhere overlooked or only hinted at in passing, something that gives creation myths but also gives you a lot more and a shortened version of a bunch of the best stories on norse mythology. It is also surprisingly short.