AD means ano domini - "in the year of our Lord [Jesus Christ]". A century is 100 years. Therefore, the first century is years 1-100, the second century 101-200, etc.
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The first century AD
The sixth century AD covers the years from 501 AD to 600 AD.
-99
125
Any year between 1501 AD and 1600 AD - including 1537 - is in the sixteenth century.