Chris Wickham's The Inheritance of Rome is a very good introduction to the period, covering the break up of the empire and subsequent histories of its successors between 400-1000, including the polities of Western Europe, the Eastern Empire, and the Caliphate. The book is intended as a more accessible follow-up to his Framing the Early Middle Ages, a titanic work that documents social and economic change in post-imperial Europe and the Mediterranean. The Inheritance of Rome focuses more on political and cultural history, but is informed by some of the the same social and economic arguments better documented in its predecessor. It's a great place to start.

Guy Halsall's Barbarian Migrations and the Roman West, 376-568 is another great survey of the break-up of the empire and the role of the barbarians therein. Peter Brown's The Rise of Western Christendom, 10th Edition covers 200-1000 and is a great introduction to the period through a cultural and religious lens.

To quote Brown, Halsall and Wickham present an image of society "unraveling," and Wickham admits in his introduction to The Inheritance of Rome his intent to find a common ground between the 'continuists' and the 'catastrophists,' the two poles of that largely bookend debate on the period. Peter Brown is often found in the continuist camp. That said, his characterization of Halsall and Wickham's position was employed as a counter-narrative to Bryan Ward-Perkins', whose The Fall of Rome and the End of Civilization is a relevant reference point for the catastrophist camp.