1)between the years of 2001 and 2010
2)between the years 2001 and 2010
3)between 2001 and 2010
4)from 2001 to 2010
Can you please tell which one of these is correct? If there are also other variants, I would be glad to see them.
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All four examples are normal usage, and perfectly reasonable.
Technically, the first three exclude the start and end years, but are often used 'inclusively' anyway, which is the only sensible interpretation for the start year in the fourth example, though even there, the end year remains ambiguous.