After having read The Inheritance of Rome: Illuminating the Dark Ages, 400-1000
by Chris Wickham
, that is now my number one referral for people who want an introduction. THIS book is for people who want to know more detail. Publication of books for the general public about the transition from the Roman world to the European world (from about 400AD to about 800AD, aka Late Antiquity, Early Medieval, Dark Ages) has been growing rapidly, reflecting a huge development over the past 30 years.
Chris Wickham's thesis is that this period is characterized by increasing regionalism and loss of an overall unifying political, cultural and social structure. He says that earlier European histories tended to start with one region (particularly Northern France) and generalize from there. This work looks at a number of regions, then after that tries to see what, if any, patterns there are. This is a social and cultural study, not a political one, so higher level politics are not analyzed. He is one of the members of the "Fall of Rome was not so cataclysmic" school, in that he notices the long-term consistencies more than the changes. He believes that many of the regional differences were already there under Roman rule, just submerged under the empire wide consistencies. He also includes Eastern Europe, the Eastern Mediterranean, and North Africa (another change from 30 years ago).
This work is focused on regions and there is very little mention of the 'barbarian migrations' mainly because in most places the effect of these was temporary and mostly at the highest political level. The Rise of Western Christendom: Triumph & Diversity 200-1000
by Peter Robert Lamont Brown
is a great companion book that covers this time. This is big picture, Cultural with a capital C, and religious history. Also try Barbarian Migrations and the Roman West, 376 - 568
by Guy Halsall
for migration history. These are all upper undergraduate, early graduate level reading. The Fall of the Roman Empire: A New History of Rome and the Barbarians
by Peter Heather takes the more cataclysmic view and is a lot easier to read. Of course there's always the classic The Decline and Fall of the Roman Empire
by Gibbon. It is still influencing people today.