This is a time period that has always fascinated me, the fall of (Western) Rome and its effects, giving way to the foundation that would bring the High Middle Ages and the Renaissance. I'm looking for some basic reading to give a good overview and maybe some medium depth stuff.
Empires and Barbarians: The Fall of Rome and the Birth of Europe by Peter Heather is a very interesting read and makes nice use of archaeological work.
From a previous post:
Peter Sarris, Empires of Faith (2011) (wonderful book on LA's political history, from 400 to 700. It is, in my opinion, the best introduction to the post-Roman world. It does include the East, though, but I think this inclusion is particularly interesting)
Peter Brown, The World of Late Antiquity: from Marcus Aurelius to Muhammad (AD 150-750) (1971, reed. 1989) (more generally, Brown's books on cultural history are brilliant)
Chris Wickham, Framing the early Middle Ages: Europe and the Mediterranean 400–800 (2005) (authoritative survey of post-Roman economy and society. Clearly one of the most interesting pieces of research of the last few years/decade on the period)
Id., The Inheritance of Rome (2009) (interestingly, it has lot of trivia and a very good eye for regional difference, though it may be lacking in overarching narratives)
To which I might add Guy Halsall's Barbarian Migrations and the Roman West, 376-568 if you are specifically interested in the “fall of Rome” proper. Heather is not bad especially, as /u/matts2 pointed out, if you are interested in archaeology. Otherwise, I don't think it is the best introduction to the period. You might also want to check Geary's books, who always does a good job to link medieval history with the modern world (case in point: The Myth of Nations: The Medieval Origins of Europe (2002)). Once again, it is not necessarily an introduction.
Unfortunately, I cannot think of similarly interesting syntheses on 9th—11th century Europe (maybe because regionalisation does not allow for an easy incorporation of, say, the Wessex monarchy and Slavic tribes in a unitary framework).
I just finished reading The Inheritance of Rome by Chris Wickham and thought it was a great overview (but a little bit lacking in details).
Georges Duby's books are easy to read and great learn from. I recommend Time of Cathedrals.