When did medieval europe start and end?

Very roughly the middle ages were from 500 C.E. to 1500 C.E. Sometimes individual will try to pin the start and end dates to specific events, such as the deposition of the last Roman emperor Romulus Augustus in 476 or the fall of Constantinople in 1453, but these division are somewhat artificial.
The middle ages can be further divided into the Early Middle ages (500-1000 CE) the High Middle ages (1000-1300 CE) and the late middle ages (1300 to 1500 CE). Just as with the start and end dates, the dates of these division are somewhat artificial, and are best seen as general benchmarks of overall social trends, rather than hard, specific dates.